Mythic squares/rectangles

[WraithX]

With a big thanks to Xyzzy, I now have my Mythic Grid scoring page available at:
http://www.mersenneforum.org/wraithx/mythic_score.html

It can score grids in any base from base-2 to base-10. It should be able to work on any size grid, but I haven't tested it larger than 30x30 base-10.

Originally Posted by R. Gerbicz

While waiting for a bus I have found a grid with +3e13 score for base=2;m=10;n=10; so you would need a terrible good scorer to verify even that small grid. For base=3; I have some not so bad result, but the larger bases are much harder.

base=10 results: (lots of these could be non-optimal)

m=10;n=10;score=1525;
0 5 1 8 7 5 0 1 0 8 
1 4 9 8 1 6 8 0 3 3 
5 0 5 4 8 1 4 3 4 1 
7 7 9 3 1 9 5 8 2 5 
2 8 0 1 2 6 5 5 3 7 
8 0 2 2 6 8 3 1 1 7 
9 9 1 3 1 4 7 2 9 3 
5 2 9 0 6 1 4 7 6 9 
4 4 6 6 5 5 2 0 7 3 
7 1 4 7 0 2 1 1 3 9

I'm not sure you're working on the same problem we are. It isn't possible to get a score of 3e13 on a base-2 10x10 grid. The maximum "digit" length of a number in a 10x10 grid is 10. For base-2, the largest 10-digit number is 2^10-1 = 1023. So you can't get a score greater than 1023.

Also, your base-10 10x10 grid has at least one fatal flaw, it does not contain the number 100. I don't think your scoring algorithm is working quite right. The problem we are working on is find how many consecutive integers are contained in the given mxn grid, and the last consecutive number is the score of the grid. The integers can be vertical (read top-to-bottom or bottom-to-top), horizontal (read from left-to-right, or right-to-left), or either diagonal (read from corner-to-corner). So, in the case of your 10x10 grid above, it gets a score of 99, since it has all integers from 1 to 99, but doesn't have 100 in it.

Also, I was able to manually improve Till's base-10 20x20 grid from 1020 up to 1040. Here is the improved grid:

[8, 1, 5, 7, 0, 5, 3, 8, 6, 4, 6, 6, 6, 2, 9, 3, 2, 6, 6, 2]
[1, 7, 8, 3, 7, 8, 6, 1, 6, 3, 2, 2, 5, 8, 5, 6, 2, 7, 0, 7]
[0, 1, 1, 1, 7, 9, 0, 8, 8, 2, 0, 6, 5, 2, 3, 3, 8, 8, 0, 3]
[1, 4, 7, 5, 7, 0, 9, 8, 1, 7, 9, 7, 5, 7, 7, 0, 6, 8, 1, 7]
[0, 3, 7, 2, 7, 5, 3, 0, 3, 6, 7, 3, 1, 2, 2, 8, 9, 8, 2, 5]
[9, 6, 2, 9, 6, 8, 1, 5, 0, 7, 8, 6, 1, 0, 1, 5, 9, 4, 2, 5]
[3, 8, 1, 1, 3, 4, 3, 0, 1, 9, 1, 2, 1, 0, 2, 6, 0, 3, 0, 1]
[5, 4, 9, 9, 1, 0, 0, 1, 8, 1, 0, 3, 2, 1, 7, 7, 8, 6, 1, 6]
[8, 4, 1, 0, 3, 8, 2, 2, 4, 2, 9, 5, 0, 0, 7, 4, 9, 4, 4, 5]
[6, 1, 0, 8, 4, 0, 2, 7, 7, 4, 7, 6, 9, 0, 3, 2, 3, 4, 5, 5]
[0, 0, 0, 0, 6, 9, 4, 9, 8, 4, 8, 9, 1, 5, 1, 4, 3, 9, 0, 2]
[6, 2, 8, 2, 1, 9, 4, 5, 5, 2, 2, 5, 1, 4, 9, 7, 3, 4, 3, 9]
[5, 7, 5, 4, 9, 9, 1, 7, 8, 7, 8, 1, 6, 2, 0, 6, 4, 6, 6, 9]
[8, 8, 8, 5, 9, 2, 2, 6, 4, 2, 4, 8, 1, 9, 5, 4, 5, 3, 1, 5]
[5, 3, 5, 1, 3, 6, 7, 6, 0, 6, 3, 7, 3, 7, 7, 6, 2, 4, 9, 6]
[4, 3, 3, 5, 3, 2, 4, 8, 4, 6, 4, 2, 3, 6, 6, 9, 5, 0, 5, 5]
[8, 7, 0, 4, 0, 1, 1, 6, 5, 0, 2, 6, 4, 3, 3, 6, 2, 4, 1, 1]
[9, 2, 9, 5, 1, 2, 4, 8, 9, 2, 3, 5, 3, 0, 1, 9, 1, 8, 0, 0]
[7, 7, 8, 4, 8, 0, 7, 2, 6, 3, 6, 7, 1, 0, 1, 0, 0, 9, 3, 2]
[2, 3, 8, 2, 7, 1, 7, 2, 8, 3, 2, 0, 1, 1, 1, 0, 1, 9, 7, 8]

[R. Gerbicz]

Originally Posted by WraithX

I'm not sure you're working on the same problem we are. It isn't possible to get a score of 3e13 on a base-2 10x10 grid.

Yes, misunderstood your puzzle, I've already used broken lines in the "word search", so you could find 100 close to the upper right corner in 10x10 grid. Now modifying my code.

ps. but this still means that where score<100 those grids are valid here also.

[Till]

Originally Posted by R. Gerbicz

Yes, misunderstood your puzzle, I've already used broken lines in the "word search", so you could find 100 close to the upper right corner in 10x10 grid. Now modifying my code.

ps. but this still means that where score<100 those grids are valid here also.

The small grids you found are very impressive. I do not doubt that when you fixed your code it will be fantastic for scores>=100, too. Great job!

[science_man_88]

something like:

• 12+4(y-2), y length connections per y by y section.
• m\y *n\y, y by y boxes before overflow (\ is floor of division)
• ((n mod y)+1) times ((m mod y)+1) places to start boxes.

probably a few things missing.

[R. Gerbicz]

Originally Posted by Till

The small grids you found are very impressive. I do not doubt that when you fixed your code it will be fantastic for scores>=100, too. Great job!

Thanks.
My results for the original puzzle in base=10:

 x |    1    2    3    4    5    6    7    8    9   10
---+--------------------------------------------------
 1 |    1    2    3    4    5    6    7    8    9   10
 2 |         4    6    8   10   21   32   37   46   54
 3 |              9   26   38   48   66   78   98  102
 4 |                  43   65   88  102  108  120  127
 5 |                       98  105  120  129  138  149
 6 |                           121  135  148  160  169
 7 |                                149  163  173  189
 8 |                                     176  194  216
 9 |                                          221  236
10 |                                               254

m=1;n=1;base=10;score=1;
1 

m=1;n=2;base=10;score=2;
1 2 

m=1;n=3;base=10;score=3;
1 3 2 

m=1;n=4;base=10;score=4;
4 1 2 3 

m=1;n=5;base=10;score=5;
4 2 5 3 1 

m=1;n=6;base=10;score=6;
5 3 1 2 6 4 

m=1;n=7;base=10;score=7;
6 5 7 3 4 1 2 

m=1;n=8;base=10;score=8;
3 4 1 6 2 8 7 5 

m=1;n=9;base=10;score=9;
7 1 4 8 2 6 5 9 3 

m=1;n=10;base=10;score=10;
7 2 9 6 5 0 1 4 8 3 

m=2;n=2;base=10;score=4;
3 4 
1 2 

m=2;n=3;base=10;score=6;
3 2 4 
1 6 5 

m=2;n=4;base=10;score=8;
1 5 8 6 
7 2 3 4 

m=2;n=5;base=10;score=10;
8 3 7 6 4 
0 1 9 5 2 

m=2;n=6;base=10;score=21;
7 9 0 1 3 6 
1 2 5 8 1 4 

m=2;n=7;base=10;score=32;
4 1 3 9 6 2 5 
8 2 2 0 1 1 7 

m=2;n=8;base=10;score=37;
3 0 1 6 5 1 2 8 
3 4 2 2 3 7 1 9 

m=2;n=9;base=10;score=46;
2 7 1 5 4 0 3 1 2 
2 8 3 6 2 4 1 3 9 

m=2;n=10;base=10;score=54;
4 0 2 8 1 7 3 6 1 4 
1 5 3 2 4 3 2 9 4 1 

m=3;n=3;base=10;score=9;
4 6 8 
2 5 7 
1 9 3 

m=3;n=4;base=10;score=26;
5 1 4 9 
3 2 1 7 
2 0 6 8 

m=3;n=5;base=10;score=38;
2 0 6 8 1 
2 1 3 2 1 
5 3 4 7 9 

m=3;n=6;base=10;score=48;
7 3 6 2 4 7 
3 1 0 4 2 8 
2 9 1 5 3 1 

m=3;n=7;base=10;score=66;
5 1 1 7 3 5 2 
6 0 2 4 5 3 8 
3 6 4 2 9 1 4 

m=3;n=8;base=10;score=78;
1 3 7 5 3 3 6 6 
8 7 0 2 4 9 5 8 
4 4 6 1 1 5 2 2 

m=3;n=9;base=10;score=98;
3 1 5 4 7 8 8 2 7 
2 0 4 6 3 1 5 9 7 
6 2 8 9 6 3 1 5 0 

m=3;n=10;base=10;score=102;
9 3 1 8 6 5 3 1 0 2 
7 4 8 2 9 3 5 0 7 4 
4 7 5 0 2 9 1 1 6 6 

m=4;n=4;base=10;score=43;
3 7 1 9 
6 1 2 5 
8 2 3 0 
9 3 4 1 

m=4;n=5;base=10;score=65;
1 1 9 4 8 
8 2 5 3 2 
2 5 0 6 3 
7 4 4 1 7 

m=4;n=6;base=10;score=88;
9 3 0 7 9 5 
4 6 3 2 1 5 
7 5 8 1 2 6 
7 8 0 4 4 6 

m=4;n=7;base=10;score=102;
1 8 8 6 6 9 9 
0 9 4 2 5 7 3 
1 0 2 4 7 5 8 
6 3 3 1 1 0 0 

m=4;n=8;base=10;score=108;
7 3 3 8 7 2 6 8 
9 7 5 1 0 6 2 8 
4 5 0 1 0 1 9 4 
6 3 2 1 1 0 4 9 

m=4;n=9;base=10;score=120;
3 3 1 7 1 1 4 6 7 
2 1 1 0 1 0 6 8 7 
6 2 0 1 9 3 4 9 2 
0 5 5 8 8 5 7 4 9 

m=4;n=10;base=10;score=127;
3 4 7 2 1 7 8 1 1 6 
4 6 8 9 5 7 1 2 2 6 
1 0 9 8 3 0 0 1 5 4 
1 1 1 2 3 1 1 5 9 4 

m=5;n=5;base=10;score=98;
8 5 9 1 2 
3 0 5 2 0 
3 6 7 4 4 
9 7 6 1 3 
4 8 8 2 1 

m=5;n=6;base=10;score=105;
7 7 0 9 4 1 
6 3 8 2 9 7 
9 4 3 1 2 5 
4 5 0 0 6 8 
5 0 1 1 8 6 

m=5;n=7;base=10;score=120;
0 2 1 1 3 3 2 
5 0 1 0 0 6 9 
7 1 1 1 6 8 5 
9 0 1 7 8 4 5 
9 4 2 2 7 3 4 

m=5;n=8;base=10;score=129;
4 5 8 6 4 8 1 3 
4 7 2 1 0 0 8 1 
6 2 1 2 1 1 9 2 
3 6 1 2 0 1 0 9 
4 9 5 5 3 3 7 7 

m=5;n=9;base=10;score=138;
8 6 4 8 1 2 4 9 9 
8 6 1 0 2 1 2 7 7 
5 7 0 1 1 1 3 1 1 
5 3 3 1 0 1 2 3 1 
4 4 1 8 9 5 8 6 9 

m=5;n=10;base=10;score=149;
5 9 7 7 6 4 1 3 9 7 
6 1 4 2 1 3 4 0 3 9 
7 6 1 1 2 1 1 1 4 1 
8 1 0 0 3 1 2 0 4 1 
8 3 1 1 7 5 9 8 5 5 

m=6;n=6;base=10;score=121;
3 7 4 1 1 7 
9 6 8 2 0 7 
5 8 6 1 2 7 
3 0 1 0 1 5 
3 1 1 0 1 5 
2 9 9 4 4 3 

m=6;n=7;base=10;score=135;
1 1 3 7 7 4 1 
6 3 8 2 1 0 4 
1 4 5 1 1 2 1 
9 5 6 2 1 0 9 
7 6 2 0 3 9 8 
8 5 0 1 1 1 8 

m=6;n=8;base=10;score=148;
6 8 1 1 2 8 8 5 
8 9 0 2 3 1 4 7 
4 5 1 1 4 1 0 6 
1 4 0 0 1 1 1 6 
6 3 1 9 2 3 2 5 
1 1 7 7 9 1 3 5 

m=6;n=9;base=10;score=160;
0 6 1 1 1 7 6 1 8 
3 0 0 1 0 5 4 5 8 
1 3 4 1 3 2 1 4 1 
2 5 1 1 1 1 1 2 1 
7 1 5 0 3 4 2 3 8 
9 7 9 8 7 9 9 6 6 

m=6;n=10;base=10;score=169;
1 4 8 8 3 6 1 9 1 2 
7 6 1 0 5 2 3 4 6 5 
1 0 6 1 2 1 0 1 4 1 
0 5 1 4 2 1 1 1 5 4 
9 3 3 3 1 8 2 5 6 7 
8 9 1 1 7 7 9 5 1 6 

m=7;n=7;base=10;score=149;
1 4 7 5 1 1 6 
0 4 1 3 1 4 5 
7 9 3 1 1 2 4 
8 1 2 1 2 6 7 
8 0 1 1 8 5 7 
1 3 0 4 0 1 5 
6 6 1 1 9 9 6 

m=7;n=8;base=10;score=163;
1 6 0 1 7 1 1 1 
9 8 1 4 5 6 3 1 
7 9 8 4 1 2 4 5 
1 2 0 3 2 1 1 0 
1 1 1 1 1 0 5 8 
6 5 4 3 0 3 1 5 
3 6 9 7 7 1 3 1 

m=7;n=9;base=10;score=173;
9 7 8 1 1 5 9 1 1 
7 9 8 1 3 4 1 6 9 
6 0 2 7 1 5 2 3 0 
1 1 1 1 0 1 1 1 7 
6 5 4 1 0 2 2 2 1 
0 8 6 4 3 3 1 5 5 
1 6 1 1 6 8 1 4 7 

m=7;n=10;base=10;score=189;
9 0 1 7 9 8 1 5 8 1 
1 3 7 1 2 9 8 2 7 1 
3 1 6 6 3 1 4 0 1 2 
8 0 1 1 2 1 1 1 2 8 
1 0 1 7 1 3 5 2 5 1 
5 6 8 5 4 3 1 6 4 5 
9 1 8 1 4 1 8 6 1 0 

m=8;n=8;base=10;score=176;
7 7 9 9 1 8 9 8 
9 0 1 5 0 1 3 6 
2 1 7 1 0 6 1 1 
1 4 3 1 1 1 4 4 
1 2 1 3 5 1 1 1 
1 2 0 1 2 5 6 4 
6 1 4 8 8 6 7 9 
4 5 1 7 2 1 1 1 

m=8;n=9;base=10;score=194;
1 3 3 1 8 1 1 6 5 
7 8 3 1 0 2 6 7 1 
1 7 2 6 2 1 1 3 0 
3 4 1 4 1 5 5 0 8 
1 2 7 1 4 0 1 8 7 
6 4 3 1 9 1 3 1 1 
2 9 8 1 1 2 6 5 1 
1 8 6 1 0 9 9 7 1 

m=8;n=10;base=10;score=216;
2 1 2 4 1 1 8 1 2 1 
1 0 8 1 8 9 1 0 0 2 
4 4 1 7 5 1 7 6 2 8 
1 3 7 1 1 5 2 1 8 3 
5 1 5 1 9 4 1 1 3 1 
0 6 6 1 6 1 3 3 9 3 
1 7 0 1 4 2 6 0 0 9 
5 0 2 2 1 0 1 9 2 1 

m=9;n=9;base=10;score=221;
5 1 7 2 9 1 5 1 7 
5 1 9 2 0 4 5 8 1 
6 7 1 0 1 6 1 9 4 
1 7 5 3 1 6 9 1 1 
8 4 4 1 6 7 3 8 2 
1 1 0 2 0 2 1 5 2 
3 3 1 2 1 0 5 1 1 
7 1 8 6 7 9 2 0 8 
1 0 8 1 4 8 1 4 2 

m=9;n=10;base=10;score=236;
8 1 2 1 1 5 3 2 1 4 
1 0 7 0 6 1 0 3 3 1 
6 8 2 4 3 7 8 2 2 0 
1 0 5 4 1 1 1 8 1 2 
9 5 1 1 7 3 1 5 2 1 
4 2 0 5 9 1 5 1 4 6 
2 0 1 1 1 8 6 1 1 6 
2 2 2 7 9 4 1 9 6 3 
6 4 5 7 2 1 0 9 2 2 

m=10;n=10;base=10;score=254;
1 9 1 0 8 8 4 2 4 9 
6 2 2 5 2 3 5 6 1 7 
8 1 1 0 4 2 1 4 5 2 
1 8 2 2 4 2 9 1 3 1 
5 3 1 6 3 1 7 1 5 0 
2 3 9 6 1 7 8 9 2 5 
0 1 0 1 1 4 1 1 4 2 
8 2 4 2 7 1 0 6 3 1 
1 4 0 3 2 0 9 0 7 5 
5 7 1 3 2 2 1 9 8 1

and after a quick search:

m=20;n=20;base=10;score=1264;
1 1 9 9 4 7 6 4 6 5 8 1 1 6 8 4 0 1 9 8 
4 2 6 8 7 5 6 8 6 8 1 2 2 2 8 1 1 0 6 5 
4 3 1 5 3 4 7 1 7 0 1 0 6 7 2 0 3 5 0 2 
8 0 1 8 2 2 1 1 2 6 1 6 4 5 0 1 0 9 4 1 
4 1 8 1 7 1 1 1 1 0 5 7 9 7 9 1 1 0 0 5 
8 5 9 8 9 0 2 1 2 3 2 6 5 9 5 6 0 6 2 1 
3 1 2 4 4 1 1 7 3 9 3 1 5 9 9 2 6 0 7 2 
9 6 2 2 1 0 7 7 7 8 6 0 1 0 3 9 1 1 3 5 
4 4 7 3 1 3 3 9 3 0 2 1 1 8 6 9 1 0 1 3 
8 8 8 7 6 8 8 0 0 1 9 0 7 0 7 5 7 2 8 6 
8 2 9 3 4 0 0 1 1 0 2 0 1 1 7 3 2 3 1 8 
3 8 6 4 7 3 1 1 1 4 1 1 1 3 5 0 4 3 1 5 
8 2 9 0 1 1 3 2 0 5 0 1 0 4 1 1 4 3 4 7 
1 9 3 1 1 2 4 8 5 8 4 3 4 7 0 1 1 2 2 4 
3 7 8 5 1 9 1 4 5 4 4 6 6 6 3 2 5 2 1 1 
1 0 0 2 1 0 4 0 4 9 9 9 3 7 4 8 1 6 2 2 
8 1 5 2 1 1 5 9 7 3 7 2 5 3 5 2 5 2 2 6 
5 0 4 5 1 0 9 8 4 5 8 9 6 5 3 4 9 6 3 2 
1 2 2 8 7 8 7 6 2 0 0 5 7 5 5 2 1 0 9 9 
1 9 8 1 0 6 6 6 1 1 1 2 7 2 3 6 1 1 9 2

[science_man_88]

Originally Posted by science_man_88

something like:

• 12+4(y-2), y length connections per y by y section.
• m\y *n\y, y by y boxes before overflow (\ is floor of division)
• ((n mod y)+1) times ((m mod y)+1) places to start boxes.

probably a few things missing.

Doh forgot overlap between boxes.

[Till]

Originally Posted by WraithX

With a big thanks to Xyzzy, I now have my Mythic Grid scoring page available at:
http://www.mersenneforum.org/wraithx/mythic_score.html

Nice page, very helpful and tolerant to various grid formats

[R. Gerbicz]

An updated table for base=10:

 x |    1    2    3    4    5    6    7    8    9   10
---+--------------------------------------------------
 1 |    1    2    3    4    5    6    7    8    9   10
 2 |         4    6    8   10   21   32   37   46   54
 3 |              9   26   38   48   66   78   98  102
 4 |                  43   65   88  102  108  120  127
 5 |                       98  105  120  130  139  150
 6 |                           123  136  148  160  175
 7 |                                149  164  177  191
 8 |                                     183  197  216
 9 |                                          221  239
10 |                                               259

m=1;n=1;base=10;score=1;
1 

m=1;n=2;base=10;score=2;
1 2 

m=1;n=3;base=10;score=3;
1 3 2 

m=1;n=4;base=10;score=4;
4 1 2 3 

m=1;n=5;base=10;score=5;
4 2 5 3 1 

m=1;n=6;base=10;score=6;
5 3 1 2 6 4 

m=1;n=7;base=10;score=7;
6 5 7 3 4 1 2 

m=1;n=8;base=10;score=8;
3 4 1 6 2 8 7 5 

m=1;n=9;base=10;score=9;
7 1 4 8 2 6 5 9 3 

m=1;n=10;base=10;score=10;
7 2 9 6 5 0 1 4 8 3 

m=2;n=2;base=10;score=4;
3 4 
1 2 

m=2;n=3;base=10;score=6;
3 2 4 
1 6 5 

m=2;n=4;base=10;score=8;
1 5 8 6 
7 2 3 4 

m=2;n=5;base=10;score=10;
8 3 7 6 4 
0 1 9 5 2 

m=2;n=6;base=10;score=21;
7 9 0 1 3 6 
1 2 5 8 1 4 

m=2;n=7;base=10;score=32;
4 1 3 9 6 2 5 
8 2 2 0 1 1 7 

m=2;n=8;base=10;score=37;
3 0 1 6 5 1 2 8 
3 4 2 2 3 7 1 9 

m=2;n=9;base=10;score=46;
2 7 1 5 4 0 3 1 2 
2 8 3 6 2 4 1 3 9 

m=2;n=10;base=10;score=54;
4 0 2 8 1 7 3 6 1 4 
1 5 3 2 4 3 2 9 4 1 

m=3;n=3;base=10;score=9;
4 6 8 
2 5 7 
1 9 3 

m=3;n=4;base=10;score=26;
5 1 4 9 
3 2 1 7 
2 0 6 8 

m=3;n=5;base=10;score=38;
2 0 6 8 1 
2 1 3 2 1 
5 3 4 7 9 

m=3;n=6;base=10;score=48;
7 3 6 2 4 7 
3 1 0 4 2 8 
2 9 1 5 3 1 

m=3;n=7;base=10;score=66;
5 1 1 7 3 5 2 
6 0 2 4 5 3 8 
3 6 4 2 9 1 4 

m=3;n=8;base=10;score=78;
1 3 7 5 3 3 6 6 
8 7 0 2 4 9 5 8 
4 4 6 1 1 5 2 2 

m=3;n=9;base=10;score=98;
3 1 5 4 7 8 8 2 7 
2 0 4 6 3 1 5 9 7 
6 2 8 9 6 3 1 5 0 

m=3;n=10;base=10;score=102;
9 3 1 8 6 5 3 1 0 2 
7 4 8 2 9 3 5 0 7 4 
4 7 5 0 2 9 1 1 6 6 

m=4;n=4;base=10;score=43;
3 7 1 9 
6 1 2 5 
8 2 3 0 
9 3 4 1 

m=4;n=5;base=10;score=65;
1 1 9 4 8 
8 2 5 3 2 
2 5 0 6 3 
7 4 4 1 7 

m=4;n=6;base=10;score=88;
9 3 0 7 9 5 
4 6 3 2 1 5 
7 5 8 1 2 6 
7 8 0 4 4 6 

m=4;n=7;base=10;score=102;
1 8 8 6 6 9 9 
0 9 4 2 5 7 3 
1 0 2 4 7 5 8 
6 3 3 1 1 0 0 

m=4;n=8;base=10;score=108;
7 3 3 8 7 2 6 8 
9 7 5 1 0 6 2 8 
4 5 0 1 0 1 9 4 
6 3 2 1 1 0 4 9 

m=4;n=9;base=10;score=120;
3 3 1 7 1 1 4 6 7 
2 1 1 0 1 0 6 8 7 
6 2 0 1 9 3 4 9 2 
0 5 5 8 8 5 7 4 9 

m=4;n=10;base=10;score=127;
3 4 7 2 1 7 8 1 1 6 
4 6 8 9 5 7 1 2 2 6 
1 0 9 8 3 0 0 1 5 4 
1 1 1 2 3 1 1 5 9 4 

m=5;n=5;base=10;score=98;
8 5 9 1 2 
3 0 5 2 0 
3 6 7 4 4 
9 7 6 1 3 
4 8 8 2 1 

m=5;n=6;base=10;score=105;
7 7 0 9 4 1 
6 3 8 2 9 7 
9 4 3 1 2 5 
4 5 0 0 6 8 
5 0 1 1 8 6 

m=5;n=7;base=10;score=120;
0 2 1 1 3 3 2 
5 0 1 0 0 6 9 
7 1 1 1 6 8 5 
9 0 1 7 8 4 5 
9 4 2 2 7 3 4 

m=5;n=8;base=10;score=130;
6 9 4 3 0 1 1 5 
1 2 5 3 2 1 0 5 
1 2 1 7 9 9 6 8 
7 1 0 0 2 6 8 3 
8 2 1 1 4 4 7 7 

m=5;n=9;base=10;score=139;
7 5 5 8 8 9 6 6 5 
9 0 1 0 1 3 1 2 8 
9 1 1 0 3 1 1 4 7 
4 2 2 1 6 2 1 3 5 
4 0 1 7 7 4 1 1 2 

m=5;n=10;base=10;score=150;
9 6 1 4 5 7 6 6 5 0 
1 3 4 3 5 8 0 1 2 5 
4 1 1 1 0 9 1 1 2 1 
7 2 3 4 1 8 0 0 1 9 
7 3 1 2 8 3 1 4 9 7 

m=6;n=6;base=10;score=123;
4 4 1 1 2 3 
7 0 1 1 3 4 
7 1 0 0 6 8 
9 2 1 6 5 7 
9 0 2 5 9 3 
8 8 1 1 4 3 

m=6;n=7;base=10;score=136;
6 7 7 4 8 9 4 
8 0 1 2 5 3 6 
8 1 1 2 1 1 4 
5 0 2 1 0 0 4 
5 3 6 3 1 2 9 
7 6 1 3 1 9 7 

m=6;n=8;base=10;score=148;
6 8 1 1 2 8 8 5 
8 9 0 2 3 1 4 7 
4 5 1 1 4 1 0 6 
1 4 0 0 1 1 1 6 
6 3 1 9 2 3 2 5 
1 1 7 7 9 1 3 5 

m=6;n=9;base=10;score=160;
0 6 1 1 1 7 6 1 8 
3 0 0 1 0 5 4 5 8 
1 3 4 1 3 2 1 4 1 
2 5 1 1 1 1 1 2 1 
7 1 5 0 3 4 2 3 8 
9 7 9 8 7 9 9 6 6 

m=6;n=10;base=10;score=175;
2 9 9 1 3 1 7 2 1 1 
4 2 1 3 0 5 4 1 5 1 
1 6 1 2 1 5 1 8 6 4 
2 3 1 1 5 3 1 7 1 6 
8 6 6 0 4 1 7 4 0 2 
9 8 0 1 0 9 5 1 4 1 

m=7;n=7;base=10;score=149;
1 4 7 5 1 1 6 
0 4 1 3 1 4 5 
7 9 3 1 1 2 4 
8 1 2 1 2 6 7 
8 0 1 1 8 5 7 
1 3 0 4 0 1 5 
6 6 1 1 9 9 6 

m=7;n=8;base=10;score=164;
9 8 8 1 1 3 3 1 
9 4 7 6 9 5 6 6 
1 4 3 0 5 1 4 2 
1 1 1 1 1 1 2 1 
6 2 1 3 2 1 0 8 
4 7 9 5 0 4 3 5 
7 5 1 0 1 1 4 1 

m=7;n=9;base=10;score=177;
2 2 1 5 9 4 7 1 8 
1 6 5 3 1 9 3 5 1 
8 1 1 7 0 6 1 4 2 
8 2 3 1 1 1 6 1 1 
4 3 1 0 2 1 0 4 7 
1 4 1 5 7 6 0 7 2 
9 2 1 1 6 7 1 8 9 

m=7;n=10;base=10;score=191;
1 9 1 3 1 1 1 9 0 9 
9 7 4 1 6 7 2 1 7 6 
8 1 2 2 0 1 5 8 3 1 
1 3 1 1 8 6 1 1 4 4 
1 3 0 8 1 1 6 0 0 1 
7 8 9 1 5 4 7 1 5 2 
7 1 4 9 1 5 5 3 1 0 

m=8;n=8;base=10;score=183;
1 8 3 0 1 2 8 1 
8 4 1 7 3 2 1 8 
1 0 2 1 3 1 6 0 
0 1 1 1 5 1 7 1 
1 4 2 5 1 0 9 7 
7 5 1 9 1 6 1 8 
9 1 6 4 3 7 3 5 
8 9 6 1 4 1 5 1 

m=8;n=9;base=10;score=197;
2 6 1 8 0 1 1 9 6 
2 2 6 7 1 5 5 8 1 
3 1 1 1 2 0 1 6 2 
1 9 4 1 8 1 5 4 5 
9 2 1 3 5 9 3 1 4 
1 3 1 9 1 7 6 0 1 
7 8 7 6 0 4 1 3 3 
4 1 7 1 0 1 8 8 1 

m=8;n=10;base=10;score=216;
2 1 2 4 1 1 8 1 2 1 
1 0 8 1 8 9 1 0 0 2 
4 4 1 7 5 1 7 6 2 8 
1 3 7 1 1 5 2 1 8 3 
5 1 5 1 9 4 1 1 3 1 
0 6 6 1 6 1 3 3 9 3 
1 7 0 1 4 2 6 0 0 9 
5 0 2 2 1 0 1 9 2 1 

m=9;n=9;base=10;score=221;
5 1 7 2 9 1 5 1 7 
5 1 9 2 0 4 5 8 1 
6 7 1 0 1 6 1 9 4 
1 7 5 3 1 6 9 1 1 
8 4 4 1 6 7 3 8 2 
1 1 0 2 0 2 1 5 2 
3 3 1 2 1 0 5 1 1 
7 1 8 6 7 9 2 0 8 
1 0 8 1 4 8 1 4 2 

m=9;n=10;base=10;score=239;
2 0 4 1 8 9 2 2 2 4 
4 3 2 3 8 2 0 3 0 1 
1 5 1 2 1 6 2 1 0 8 
1 4 1 9 6 0 1 7 9 1 
6 3 4 1 5 8 5 8 1 1 
3 1 5 0 4 1 6 1 3 9 
2 5 7 1 6 7 3 2 0 9 
2 3 8 9 1 1 1 7 0 2 
5 2 9 3 3 2 7 7 1 1 

m=10;n=10;base=10;score=259;
2 7 1 7 3 6 1 8 1 4 
5 6 6 5 8 3 7 8 4 4 
0 7 9 1 9 2 2 1 3 2 
3 0 1 9 1 1 2 0 2 2 
2 0 8 0 1 9 2 1 0 6 
6 1 5 1 7 4 3 4 6 1 
2 5 2 1 7 1 2 1 5 5 
2 4 2 5 3 1 4 8 1 3 
3 5 0 4 1 6 6 7 3 2 
9 2 7 1 9 8 3 1 0 2

Originally Posted by Till

The record score for 6x6 squares in base 2 seems to be 42.
Example:

[0, 1, 1, 1, 1, 1]
[1, 0, 0, 0, 0, 0]
[1, 1, 1, 0, 1, 0]
[0, 0, 0, 0, 0, 1]
[0, 0, 1, 1, 0, 1]
[1, 0, 0, 0, 1, 1]

And the best 7x7 score might be 64, example:

[1, 0, 1, 0, 0, 0, 1]
[1, 1, 0, 1, 1, 0, 1]
[1, 1, 0, 1, 0, 1, 0]
[1, 1, 0, 1, 1, 1, 0]
[0, 1, 0, 0, 1, 0, 0]
[0, 1, 0, 0, 1, 1, 0]
[1, 1, 0, 0, 0, 1, 1]

The first 6x6 square with score 42 turned up after testing 300k squares, nothing new within 10 mio square tests. So I am quite confident that it has the maximum score.

The first 7x7 square with score 64 turned up after testing 15mio squares, nothing new within 63.7 mio square tests. Less confidence here, but still some (75% maybe).

So the central term sequence might be 1, 3, 7, 15, 26, 42, 64, ...
The only possible match in OEIS is A131076 then.

My best results for base=2:

 x |    1    2    3    4    5    6    7    8    9   10
---+--------------------------------------------------
 1 |    1    2    3    4    4    6    7    8    8    8
 2 |         3    5    6    8   10   15   16   16   20
 3 |              7   10   13   16   16   20   23   32
 4 |                  15   18   20   22   27   32   37
 5 |                       26   32   36   38   44   46
 6 |                            44   55   64   68   72
 7 |                                 69   77   87   95
 8 |                                      89  109  128
 9 |                                          130  141
10 |                                               153

m=1;n=1;base=2;score=1;
1 

m=1;n=2;base=2;score=2;
1 0 

m=1;n=3;base=2;score=3;
0 1 1 

m=1;n=4;base=2;score=4;
0 0 1 1 

m=1;n=5;base=2;score=4;
1 1 0 0 1 

m=1;n=6;base=2;score=6;
0 0 1 0 1 1 

m=1;n=7;base=2;score=7;
0 0 1 0 1 1 1 

m=1;n=8;base=2;score=8;
1 0 1 1 1 0 0 0 

m=1;n=9;base=2;score=8;
1 0 1 1 1 1 0 0 0 

m=1;n=10;base=2;score=8;
1 1 1 1 0 0 0 1 0 1 

m=2;n=2;base=2;score=3;
1 0 
1 0 

m=2;n=3;base=2;score=5;
1 0 1 
1 0 0 

m=2;n=4;base=2;score=6;
1 0 0 1 
1 0 1 1 

m=2;n=5;base=2;score=8;
1 0 1 1 1 
1 0 0 0 1 

m=2;n=6;base=2;score=10;
1 1 1 0 0 1 
0 0 0 1 0 1 

m=2;n=7;base=2;score=15;
0 0 0 1 1 1 1 
1 1 0 1 0 0 1 

m=2;n=8;base=2;score=16;
1 0 0 1 1 0 1 0 
1 1 1 1 0 0 0 0 

m=2;n=9;base=2;score=16;
1 1 0 1 0 0 0 0 0 
0 1 0 0 1 1 1 1 1 

m=2;n=10;base=2;score=20;
1 1 1 1 0 1 0 0 0 0 
0 1 0 0 0 1 0 0 1 1 

m=3;n=3;base=2;score=7;
1 0 1 
0 1 0 
1 1 0 

m=3;n=4;base=2;score=10;
0 0 0 1 
0 1 0 1 
1 0 0 1 

m=3;n=5;base=2;score=13;
1 0 0 1 1 
1 1 0 1 0 
1 0 0 0 1 

m=3;n=6;base=2;score=16;
1 1 1 1 0 1 
1 1 0 0 0 0 
1 0 0 1 0 1 

m=3;n=7;base=2;score=16;
1 1 1 1 0 1 0 
0 1 0 0 0 0 0 
1 0 1 1 0 0 1 

m=3;n=8;base=2;score=20;
0 1 1 1 1 0 0 1 
0 0 0 0 1 0 1 1 
1 0 0 0 1 0 0 1 

m=3;n=9;base=2;score=23;
1 1 0 0 1 0 0 0 0 
1 1 1 1 1 0 1 1 0 
1 0 1 0 1 0 0 0 1 

m=3;n=10;base=2;score=32;
1 1 0 0 1 0 1 0 1 1 
0 0 0 0 0 1 1 1 1 1 
1 1 1 0 1 1 0 0 0 1 

m=4;n=4;base=2;score=15;
1 0 0 0 
1 0 1 1 
1 1 0 0 
1 1 0 1 

m=4;n=5;base=2;score=18;
1 0 0 0 1 
1 0 1 1 1 
1 0 0 1 0 
1 0 0 0 0 

m=4;n=6;base=2;score=20;
1 1 1 0 0 1 
1 0 0 0 1 1 
1 0 0 0 0 0 
1 0 0 1 0 1 

m=4;n=7;base=2;score=22;
1 1 1 0 0 1 0 
0 1 1 0 1 0 1 
1 0 1 0 0 0 1 
1 0 1 0 0 0 0 

m=4;n=8;base=2;score=27;
1 1 1 0 1 0 1 1 
1 1 0 1 1 0 0 1 
0 0 0 0 1 0 0 1 
1 1 0 0 0 1 0 1 

m=4;n=9;base=2;score=32;
1 1 0 1 1 0 0 0 1 
1 1 1 1 1 0 1 0 1 
0 1 0 1 0 0 1 1 1 
0 1 0 0 0 0 0 0 0 

m=4;n=10;base=2;score=37;
1 1 1 1 1 0 0 0 0 1 
1 1 0 1 1 0 0 0 0 0 
1 1 1 0 1 0 1 0 0 1 
1 1 0 0 1 0 0 0 1 1 

m=5;n=5;base=2;score=26;
0 0 1 0 1 
1 1 0 0 0 
0 1 0 0 1 
1 0 1 0 1 
1 1 1 1 1 

m=5;n=6;base=2;score=32;
1 1 1 1 1 0 
0 1 1 0 1 1 
1 0 1 0 1 1 
1 0 0 0 0 0 
1 0 0 1 0 1 

m=5;n=7;base=2;score=36;
1 0 0 0 0 1 0 
0 0 0 0 0 1 1 
1 1 0 0 1 0 0 
0 1 0 0 0 1 1 
1 0 1 1 1 1 1 

m=5;n=8;base=2;score=38;
1 1 0 0 0 0 0 1 
1 0 0 0 0 1 1 1 
0 1 1 0 0 1 0 1 
1 0 0 1 0 0 0 1 
1 1 1 1 0 0 0 1 

m=5;n=9;base=2;score=44;
0 1 0 0 0 1 1 1 1 
0 0 0 0 0 1 0 0 1 
1 1 0 1 0 0 0 0 1 
1 1 0 1 0 1 0 0 1 
1 1 1 0 0 1 1 0 1 

m=5;n=10;base=2;score=46;
1 0 1 0 1 0 1 1 0 1 
1 0 0 1 1 0 0 0 0 1 
1 1 0 0 1 0 0 0 0 0 
1 0 1 1 1 0 0 1 0 1 
1 0 1 1 0 0 0 1 0 1 

m=6;n=6;base=2;score=44;
1 0 1 0 1 1 
1 0 0 1 0 1 
1 1 0 0 0 1 
1 1 1 0 0 1 
1 0 1 0 0 0 
0 1 0 1 0 1 

m=6;n=7;base=2;score=55;
1 1 0 0 1 1 1 
1 1 0 1 0 0 1 
0 1 0 0 0 1 1 
0 1 1 1 0 1 1 
1 1 0 0 0 0 0 
0 0 1 1 0 1 1 

m=6;n=8;base=2;score=64;
1 0 1 1 1 1 1 1 
1 1 0 0 0 0 0 0 
1 0 0 1 0 1 1 1 
0 0 1 0 0 1 1 0 
0 0 0 1 1 1 1 0 
1 1 1 0 1 1 0 0 

m=6;n=9;base=2;score=68;
1 1 1 1 1 1 1 0 1 
0 1 0 0 0 0 1 1 1 
1 0 1 0 0 0 0 0 0 
0 0 1 1 0 1 1 1 0 
1 1 0 0 0 0 0 1 1 
0 0 1 0 0 0 1 1 1 

m=6;n=10;base=2;score=72;
1 1 1 1 0 0 0 0 0 0 
1 0 1 0 0 0 1 1 1 1 
1 0 0 1 0 0 0 1 1 0 
1 1 0 0 0 0 1 0 1 1 
1 0 1 1 0 0 0 0 0 1 
1 0 1 1 0 1 1 1 1 1 

m=7;n=7;base=2;score=69;
1 1 1 1 1 1 1 
1 0 1 1 0 0 1 
1 0 0 0 0 0 0 
1 0 1 0 0 0 1 
1 0 1 1 0 1 1 
0 0 1 0 1 1 1 
0 1 0 1 0 1 1 

m=7;n=8;base=2;score=77;
1 1 1 0 1 1 1 0 
1 0 0 1 0 0 0 1 
0 1 0 0 0 0 1 1 
0 1 0 1 0 1 1 1 
1 0 0 0 1 1 1 1 
1 1 0 0 1 0 0 1 
1 1 1 1 0 0 1 1 

m=7;n=9;base=2;score=87;
1 1 1 0 1 1 1 0 0 
1 0 1 0 0 0 0 1 1 
1 0 1 0 0 1 1 1 0 
0 1 1 0 1 0 1 0 1 
1 0 1 0 0 1 0 0 1 
0 1 0 0 1 0 0 0 1 
1 1 1 1 0 0 1 1 1 

m=7;n=10;base=2;score=95;
1 1 1 1 1 1 1 0 0 1 
0 0 1 0 0 1 0 1 0 1 
1 0 1 0 0 0 1 1 0 1 
1 1 0 1 0 0 0 0 1 1 
1 1 1 0 1 1 1 0 0 1 
1 0 0 1 0 0 1 1 0 0 
0 1 0 1 0 1 1 0 1 1 

m=8;n=8;base=2;score=89;
0 1 1 1 0 1 1 0 
1 0 0 1 1 0 1 1 
1 0 1 1 0 0 0 1 
1 0 0 1 0 0 1 0 
1 1 1 0 0 1 0 1 
0 1 0 1 0 0 0 0 
0 1 0 0 0 0 1 1 
1 1 1 1 1 1 0 1 

m=8;n=9;base=2;score=109;
1 1 1 1 0 1 0 1 1 
1 0 1 0 1 1 1 1 0 
0 0 0 0 0 0 0 0 1 
0 1 0 0 1 0 1 0 0 
1 1 0 1 1 0 1 0 1 
1 1 0 0 1 1 0 0 0 
1 0 0 0 0 1 0 1 1 
1 1 1 1 1 1 0 1 1 

m=8;n=10;base=2;score=128;
1 1 1 0 1 1 1 1 1 1 
0 0 1 0 1 0 0 0 1 1 
1 1 0 1 0 1 0 1 0 0 
1 0 0 1 1 0 1 1 0 0 
1 0 0 0 0 1 0 1 1 1 
0 1 1 0 1 1 0 0 0 1 
1 1 1 1 1 0 0 0 0 1 
1 1 1 1 1 1 1 0 1 0 

m=9;n=9;base=2;score=130;
1 1 1 1 1 1 1 1 1 
0 0 1 0 1 1 1 1 0 
1 0 1 1 0 1 0 1 1 
0 0 0 0 0 1 0 1 1 
1 1 0 0 1 1 1 0 1 
0 1 1 0 0 0 1 0 0 
1 1 0 0 0 0 0 0 1 
1 0 1 0 0 1 0 0 1 
1 1 1 1 1 1 0 1 1 

m=9;n=10;base=2;score=141;
1 0 1 1 0 0 0 1 0 0 
1 0 0 0 0 1 1 1 1 1 
1 1 1 1 0 1 0 0 0 1 
1 0 1 0 0 0 0 1 0 0 
1 0 1 1 0 1 0 1 1 1 
1 0 0 0 0 1 0 0 0 1 
1 1 0 0 0 1 1 0 0 1 
0 1 1 1 1 0 1 1 0 1 
1 1 1 0 0 1 0 1 1 1 

m=10;n=10;base=2;score=153;
1 1 1 0 0 1 1 1 1 1 
0 0 0 0 0 0 0 1 0 1 
1 1 0 1 1 0 1 0 0 1 
1 0 0 0 1 0 0 0 1 1 
1 0 1 1 1 0 0 1 1 0 
1 0 0 0 0 1 1 0 0 1 
1 1 0 0 0 0 0 1 0 1 
1 1 1 1 0 0 0 0 1 1 
1 0 1 0 1 1 1 1 0 0 
0 1 1 0 1 0 1 1 0 1

Surprisingly there is an easy computer proof that we can't do better for m=n=6: so there is no grid for score=45: we can't even place the numbers from [32,45] on the long full lines (row,column,diagonal), note that these has got 6 bits in base two, so we have to place these on the full lines.

For m=n=7 I've a longer optimized search proof, first placing the numbers from [64,70] in the full long lines in all possible ways, using square symmetry resulted that we have to check "only" ~4 billion grids. And that is easy, much easier than a lazy approach of 2^(m*n)=2^49 grids checking. With a similar short search I was able to rediscover the m=n=6, score=44 solution.

[Till]

So I've been a bit too quick on my predictions for 6x6 and 7x7 in base 2. Then there seem to be no OEIS matches for any of the sequences in the base 2 table.


Your fixed code results really look very good. I improved my own code but it's still no match at all; my topscore for a 20x20 in base 10 is just 1098 now...

[R. Gerbicz]

From my improved code:
base two results: probably optimal for m,n<8 and also for m=n=8.

 x |    1    2    3    4    5    6    7    8    9   10
---+--------------------------------------------------
 1 |    1    2    3    4    4    6    7    8    8    8
 2 |         3    5    6    8   10   15   16   16   20
 3 |              7   10   13   16   16   20   23   32
 4 |                  15   18   20   22   27   32   37
 5 |                       26   32   36   38   44   46
 6 |                            44   55   64   68   72
 7 |                                 69   78   87   99
 8 |                                      92  119  133
 9 |                                          135  150
10 |                                               165

m=1;n=1;base=2;score=1;
1 

m=1;n=2;base=2;score=2;
1 0 

m=1;n=3;base=2;score=3;
0 1 1 

m=1;n=4;base=2;score=4;
0 0 1 1 

m=1;n=5;base=2;score=4;
0 0 1 1 1 

m=1;n=6;base=2;score=6;
0 0 1 0 1 1 

m=1;n=7;base=2;score=7;
0 0 1 1 1 0 1 

m=1;n=8;base=2;score=8;
0 0 0 1 0 1 1 1 

m=1;n=9;base=2;score=8;
0 0 0 1 1 1 0 1 0 

m=1;n=10;base=2;score=8;
1 1 0 1 0 0 0 1 1 1 

m=2;n=2;base=2;score=3;
0 1 
1 1 

m=2;n=3;base=2;score=5;
0 0 1 
1 0 1 

m=2;n=4;base=2;score=6;
1 0 0 1 
1 1 0 1 

m=2;n=5;base=2;score=8;
1 0 1 1 1 
1 1 0 0 0 

m=2;n=6;base=2;score=10;
1 0 1 0 0 1 
0 0 0 1 1 1 

m=2;n=7;base=2;score=15;
1 1 0 1 0 0 1 
1 1 1 1 0 0 0 

m=2;n=8;base=2;score=16;
0 1 0 1 1 0 0 1 
1 1 1 1 0 0 0 0 

m=2;n=9;base=2;score=16;
0 0 0 0 1 1 0 0 1 
1 1 1 1 1 1 0 1 0 

m=2;n=10;base=2;score=20;
0 1 1 0 0 1 0 0 0 1 
1 1 1 1 0 1 0 0 0 0 

m=3;n=3;base=2;score=7;
1 0 1 
0 1 1 
0 0 1 

m=3;n=4;base=2;score=10;
1 0 0 0 
1 0 1 0 
1 0 0 1 

m=3;n=5;base=2;score=13;
1 0 0 1 1 
1 1 0 1 0 
1 0 0 0 1 

m=3;n=6;base=2;score=16;
1 0 1 1 1 1 
1 1 0 0 0 0 
1 0 1 0 0 1 

m=3;n=7;base=2;score=16;
1 1 0 1 0 0 0 
0 0 0 0 0 1 1 
1 0 0 1 1 1 1 

m=3;n=8;base=2;score=20;
1 0 0 0 1 0 1 1 
1 0 0 1 0 0 0 0 
1 0 0 1 1 1 1 1 

m=3;n=9;base=2;score=23;
1 0 0 0 1 0 0 0 0 
0 1 1 0 1 0 0 1 1 
1 1 0 1 0 1 1 1 1 

m=3;n=10;base=2;score=32;
1 1 1 1 1 0 0 0 0 0 
0 1 0 0 1 1 0 1 1 1 
1 1 0 1 0 1 0 0 0 1 

m=4;n=4;base=2;score=15;
1 1 1 1 
1 0 0 0 
1 1 0 0 
0 1 1 1 

m=4;n=5;base=2;score=18;
1 0 0 0 1 
1 0 0 1 0 
0 0 0 0 1 
0 1 1 1 1 

m=4;n=6;base=2;score=20;
0 0 1 0 1 1 
0 0 0 0 1 1 
1 0 0 0 1 1 
1 1 0 0 1 0 

m=4;n=7;base=2;score=22;
1 1 0 0 0 0 1 
1 0 1 0 1 1 0 
1 0 1 0 0 1 1 
1 1 1 0 0 0 1 

m=4;n=8;base=2;score=27;
1 0 0 1 0 0 0 0 
1 1 0 1 1 0 0 1 
1 1 0 0 0 1 0 1 
1 1 0 1 0 1 1 1 

m=4;n=9;base=2;score=32;
1 0 1 0 1 1 1 1 1 
1 1 0 1 1 0 0 0 1 
1 1 0 0 0 0 0 0 0 
0 1 0 1 0 0 1 1 1 

m=4;n=10;base=2;score=37;
1 1 0 0 1 0 0 0 0 0 
1 1 0 1 1 0 0 0 1 0 
1 1 1 0 1 0 1 0 0 1 
1 0 0 0 0 1 1 1 1 1 

m=5;n=5;base=2;score=26;
0 1 1 0 1 
1 1 0 0 0 
0 1 0 0 1 
1 0 1 0 0 
1 1 1 1 1 

m=5;n=6;base=2;score=32;
1 0 1 1 1 1 
1 1 0 1 0 1 
1 0 0 1 1 1 
0 0 0 0 0 1 
0 1 1 0 1 1 

m=5;n=7;base=2;score=36;
1 0 0 0 0 1 1 
1 1 0 0 0 0 0 
0 0 1 0 0 1 1 
1 1 0 0 0 1 0 
1 1 1 1 1 0 1 

m=5;n=8;base=2;score=38;
1 0 0 0 1 1 1 1 
1 0 0 0 0 1 1 1 
1 0 1 0 0 1 1 0 
1 0 0 1 0 0 0 1 
1 0 0 0 0 0 1 1 

m=5;n=9;base=2;score=44;
1 1 0 1 0 0 0 1 1 
1 0 0 0 0 1 0 0 1 
1 1 1 1 0 0 0 0 0 
1 0 1 1 0 0 1 1 1 
1 1 0 1 0 1 0 0 1 

m=5;n=10;base=2;score=46;
1 0 1 1 0 1 0 1 0 1 
1 0 0 0 0 1 0 0 1 1 
1 0 0 1 1 0 0 0 0 0 
1 0 1 1 0 0 0 1 0 1 
1 0 1 1 1 0 0 1 0 1 

m=6;n=6;base=2;score=44;
0 1 1 1 1 1 
1 0 1 1 0 0 
0 1 1 0 0 1 
1 0 0 0 1 0 
0 0 0 0 0 1 
1 0 1 1 1 1 

m=6;n=7;base=2;score=55;
1 1 1 0 0 1 1 
1 0 0 1 0 1 1 
1 1 0 0 0 1 0 
1 1 0 1 1 1 0 
0 0 0 0 0 1 1 
1 1 0 1 1 0 0 

m=6;n=8;base=2;score=64;
1 1 0 1 1 1 1 1 
0 0 0 0 0 0 1 1 
1 0 1 1 0 1 1 0 
0 0 1 0 0 1 1 0 
0 0 1 0 1 1 1 0 
0 1 1 1 0 0 1 1 

m=6;n=9;base=2;score=68;
1 1 1 1 1 1 1 0 1 
0 1 0 0 0 0 1 1 1 
1 0 1 0 0 0 0 0 0 
0 0 1 1 0 1 1 1 0 
1 1 0 0 0 0 0 1 1 
0 0 1 0 0 0 1 1 1 

m=6;n=10;base=2;score=72;
1 1 1 1 0 0 0 0 0 0 
1 0 1 0 0 0 1 1 1 1 
1 0 0 1 0 0 0 1 1 0 
1 1 0 0 0 0 1 0 1 1 
1 0 1 1 0 0 0 0 0 1 
1 0 1 1 0 1 1 1 1 1 

m=7;n=7;base=2;score=69;
1 1 1 1 1 1 1 
1 0 1 1 0 0 1 
1 0 0 0 0 0 0 
1 0 1 0 0 0 1 
1 0 1 1 0 1 1 
0 0 1 0 1 1 1 
0 1 0 1 0 1 1 

m=7;n=8;base=2;score=78;
1 1 0 0 1 1 1 0 
1 0 0 1 0 0 1 1 
1 1 1 1 0 0 0 1 
1 1 1 0 1 0 1 0 
1 1 0 0 0 0 1 0 
1 0 0 0 1 0 0 1 
1 1 1 1 1 0 1 1 

m=7;n=9;base=2;score=87;
1 1 1 0 1 1 1 0 0 
1 0 1 0 0 0 0 1 1 
1 0 1 0 0 1 1 1 0 
0 1 1 0 1 0 1 0 1 
1 0 1 0 0 1 0 0 1 
0 1 0 0 1 0 0 0 1 
1 1 1 1 0 0 1 1 1 

m=7;n=10;base=2;score=99;
1 1 1 1 1 0 1 1 1 1 
1 0 0 0 0 1 0 1 0 1 
1 0 0 1 0 0 0 1 1 1 
0 1 0 1 0 0 1 1 1 0 
0 1 0 1 0 1 1 0 1 1 
1 0 1 1 0 0 0 0 0 0 
1 0 1 0 1 1 1 1 1 1 

m=8;n=8;base=2;score=92;
1 1 1 0 1 1 0 1 
1 1 0 1 0 0 1 0 
0 1 0 0 0 0 0 0 
1 1 1 0 0 1 0 1 
1 0 1 0 1 0 1 1 
1 0 1 0 1 1 0 1 
1 0 0 1 0 0 0 1 
1 1 1 1 1 1 1 1 

m=8;n=9;base=2;score=119;
1 0 1 1 0 0 0 1 1 
1 1 1 0 0 1 1 0 0 
1 0 0 0 0 0 0 0 1 
0 1 0 1 1 1 0 0 1 
1 1 0 0 0 0 1 0 1 
1 0 1 0 1 0 1 0 0 
0 1 0 1 1 1 1 1 1 
0 1 1 1 1 0 1 1 1 

m=8;n=10;base=2;score=133;
0 1 1 1 1 1 1 1 0 1 
0 1 0 0 0 0 0 1 1 1 
0 0 1 0 0 0 0 1 0 1 
1 0 1 1 0 1 0 1 0 0 
1 1 1 1 0 1 0 0 1 1 
1 1 0 0 0 1 0 0 1 1 
1 0 1 1 0 0 0 1 1 1 
1 0 1 1 0 1 1 1 1 0 

m=9;n=9;base=2;score=135;
1 1 0 1 1 0 0 1 1 
0 1 1 1 1 0 1 0 1 
1 0 1 0 1 0 0 1 0 
1 0 1 1 1 0 0 1 0 
0 1 0 0 0 0 0 1 1 
1 0 1 1 0 0 0 0 1 
1 0 0 1 0 0 0 1 1 
1 1 0 0 0 1 0 1 1 
1 0 1 1 1 1 1 1 1 

m=9;n=10;base=2;score=150;
1 1 1 1 1 1 1 1 0 1 
1 0 1 0 0 1 0 0 1 1 
0 0 1 0 0 0 1 0 0 0 
1 1 0 0 0 0 1 0 0 1 
0 0 1 0 1 0 0 1 1 1 
1 1 1 0 1 0 0 0 1 1 
1 1 0 0 1 1 0 0 0 1 
1 0 1 1 1 0 1 1 1 0 
1 1 0 0 1 1 1 0 1 0 

m=10;n=10;base=2;score=165;
1 1 1 1 0 1 1 0 1 0 
1 1 1 0 1 0 0 1 0 1 
1 0 1 0 1 0 0 1 0 0 
1 1 1 0 0 1 0 0 1 0 
0 1 1 0 0 0 1 0 1 1 
1 0 0 1 0 1 1 0 0 1 
1 0 1 0 0 0 1 0 0 1 
1 0 0 0 1 0 0 0 0 1 
0 1 1 1 0 0 0 0 1 0 
1 0 0 1 1 1 1 1 1 1

[R. Gerbicz]

Stopped my search, updating all tables:

base two:

 x |    1    2    3    4    5    6    7    8    9   10
---+--------------------------------------------------
 1 |    1    2    3    4    4    6    7    8    8    8
 2 |         3    5    6    8   10   15   16   16   20
 3 |              7   10   13   16   16   20   23   32
 4 |                  15   18   20   22   27   32   37
 5 |                       26   32   36   38   44   46
 6 |                            44   55   64   68   72
 7 |                                 69   78   87   99
 8 |                                      92  119  133
 9 |                                          135  152
10 |                                               167

m=1;n=1;base=2;score=1;
1 

m=1;n=2;base=2;score=2;
1 0 

m=1;n=3;base=2;score=3;
0 1 1 

m=1;n=4;base=2;score=4;
1 1 0 0 

m=1;n=5;base=2;score=4;
1 1 1 0 0 

m=1;n=6;base=2;score=6;
1 0 1 1 0 0 

m=1;n=7;base=2;score=7;
0 0 1 0 1 1 1 

m=1;n=8;base=2;score=8;
1 1 1 0 1 0 0 0 

m=1;n=9;base=2;score=8;
1 1 0 1 1 1 0 0 0 

m=1;n=10;base=2;score=8;
1 0 1 1 0 0 0 1 1 1 

m=2;n=2;base=2;score=3;
1 1 
0 0 

m=2;n=3;base=2;score=5;
1 0 1 
0 0 1 

m=2;n=4;base=2;score=6;
1 0 0 0 
1 1 0 1 

m=2;n=5;base=2;score=8;
1 0 0 0 0 
1 0 1 1 1 

m=2;n=6;base=2;score=10;
1 1 1 0 0 1 
1 0 1 0 0 0 

m=2;n=7;base=2;score=15;
1 1 0 1 0 0 1 
0 0 0 1 1 1 1 

m=2;n=8;base=2;score=16;
1 1 1 1 0 0 0 0 
1 0 0 1 0 1 1 1 

m=2;n=9;base=2;score=16;
0 1 0 1 1 0 0 0 0 
0 1 1 1 1 1 0 0 1 

m=2;n=10;base=2;score=20;
1 1 0 0 1 0 1 1 1 1 
0 0 0 0 1 1 0 0 0 1 

m=3;n=3;base=2;score=7;
1 0 1 
0 1 1 
0 0 1 

m=3;n=4;base=2;score=10;
0 0 0 1 
0 1 0 1 
1 0 0 1 

m=3;n=5;base=2;score=13;
1 1 0 0 1 
0 1 0 1 1 
0 1 0 0 0 

m=3;n=6;base=2;score=16;
1 0 0 1 0 1 
1 1 0 0 0 0 
1 1 1 1 0 1 

m=3;n=7;base=2;score=16;
0 1 0 1 0 0 1 
1 1 0 0 0 0 1 
1 0 1 1 1 1 0 

m=3;n=8;base=2;score=20;
0 1 1 0 0 0 0 1 
1 0 0 0 1 0 1 1 
1 1 1 1 0 0 1 0 

m=3;n=9;base=2;score=23;
0 1 1 0 1 0 0 0 0 
1 1 0 0 1 0 0 0 1 
1 1 1 1 1 0 1 0 1 

m=3;n=10;base=2;score=32;
0 0 0 0 0 1 1 1 1 1 
0 1 0 0 1 1 0 1 1 1 
1 0 0 0 1 0 1 0 1 1 

m=4;n=4;base=2;score=15;
0 1 1 1 
1 1 1 1 
1 0 0 0 
1 0 0 1 

m=4;n=5;base=2;score=18;
0 1 0 0 1 
1 0 0 0 0 
1 1 1 1 0 
1 0 0 0 1 

m=4;n=6;base=2;score=20;
1 0 0 0 1 1 
0 0 0 0 1 1 
1 1 0 0 1 1 
1 0 0 1 0 1 

m=4;n=7;base=2;score=22;
1 0 1 0 0 1 1 
0 1 1 0 0 0 1 
1 0 1 0 0 0 0 
1 0 1 0 1 1 0 

m=4;n=8;base=2;score=27;
1 1 0 1 0 1 1 1 
1 0 0 1 1 0 1 1 
1 0 0 1 0 0 0 0 
1 0 1 0 0 0 1 1 

m=4;n=9;base=2;score=32;
1 0 0 0 1 1 1 1 1 
0 0 0 0 0 0 0 1 1 
1 1 0 0 1 0 1 1 1 
1 0 1 0 1 1 0 1 1 

m=4;n=10;base=2;score=37;
1 1 0 1 1 0 0 0 0 1 
1 1 0 0 1 0 0 0 1 1 
0 0 0 0 0 1 1 1 1 1 
1 0 0 1 0 1 0 1 1 1 

m=5;n=5;base=2;score=26;
1 1 0 0 0 
1 0 1 1 1 
1 0 1 0 0 
1 0 0 0 1 
1 0 0 1 1 

m=5;n=6;base=2;score=32;
1 1 1 1 1 0 
0 0 0 0 0 1 
1 1 0 1 1 0 
0 1 1 0 1 0 
1 1 0 0 0 1 

m=5;n=7;base=2;score=36;
0 0 1 0 0 1 1 
0 1 0 0 0 1 1 
1 1 1 1 1 0 0 
0 0 0 0 0 1 1 
1 1 0 0 0 0 1 

m=5;n=8;base=2;score=38;
1 0 0 0 1 1 1 1 
1 0 0 0 1 0 0 1 
1 0 1 0 0 1 1 0 
1 1 1 0 0 0 0 1 
1 0 0 0 0 0 1 1 

m=5;n=9;base=2;score=44;
1 0 0 1 0 1 0 1 1 
0 0 0 0 0 1 0 1 1 
1 1 1 0 0 1 1 0 1 
1 0 1 0 0 0 0 1 1 
1 0 0 1 0 0 0 1 1 

m=5;n=10;base=2;score=46;
1 0 1 1 1 0 0 1 0 1 
1 0 1 0 0 0 1 1 0 1 
1 0 0 0 0 1 1 0 0 1 
1 0 0 1 0 0 0 0 0 1 
0 1 0 1 0 1 1 0 1 1 

m=6;n=6;base=2;score=44;
0 1 0 1 0 1 
1 0 1 0 0 0 
1 1 1 0 0 1 
1 1 0 0 0 1 
1 0 0 1 0 1 
1 0 1 0 1 1 

m=6;n=7;base=2;score=55;
1 1 1 0 0 1 1 
1 0 0 1 0 1 1 
1 1 0 0 0 1 0 
1 1 0 1 1 1 0 
0 0 0 0 0 1 1 
1 1 0 1 1 0 0 

m=6;n=8;base=2;score=64;
1 1 1 1 1 1 0 0 
1 1 0 0 0 0 0 0 
1 0 1 0 1 1 1 1 
0 0 0 0 0 1 0 1 
1 1 1 0 0 1 0 0 
1 1 0 1 1 0 0 1 

m=6;n=9;base=2;score=68;
0 1 1 1 0 1 1 0 1 
1 1 1 0 0 0 1 0 0 
0 0 0 0 0 0 1 1 0 
0 1 0 1 1 1 1 1 1 
1 0 1 0 0 0 0 0 1 
1 1 1 0 0 0 0 1 0 

m=6;n=10;base=2;score=72;
1 0 0 0 0 0 1 1 1 1 
0 1 1 0 0 0 1 0 0 1 
0 1 0 0 0 0 1 1 0 1 
1 1 0 0 0 0 0 0 1 1 
1 0 1 1 0 1 1 1 1 1 
1 1 1 1 0 0 0 1 0 1 

m=7;n=7;base=2;score=69;
1 1 1 1 0 1 0 
0 0 1 0 0 1 1 
1 0 0 0 0 1 1 
1 1 1 0 0 1 1 
1 1 0 1 0 0 1 
0 0 1 0 0 0 1 
1 1 0 1 1 0 1 

m=7;n=8;base=2;score=78;
1 1 0 0 1 1 1 0 
1 0 0 1 0 0 1 1 
1 1 1 1 0 0 0 1 
1 0 1 0 1 0 1 1 
1 1 0 0 0 0 1 0 
1 0 0 0 1 0 0 1 
1 1 1 1 1 0 1 1 

m=7;n=9;base=2;score=87;
1 1 1 1 1 1 0 0 1 
0 1 0 0 0 0 0 1 0 
1 0 1 0 0 0 1 1 0 
0 1 0 0 1 0 1 0 1 
1 1 1 0 0 1 0 1 1 
1 0 0 1 0 0 0 0 1 
1 1 1 1 1 0 1 1 0 

m=7;n=10;base=2;score=99;
0 0 1 1 0 0 1 1 1 1 
1 1 1 0 0 0 0 0 0 0 
1 1 0 1 0 0 0 1 1 1 
0 1 0 0 1 0 1 0 1 0 
1 0 0 1 0 1 1 0 1 1 
1 0 1 1 0 0 0 1 0 0 
1 0 1 0 1 1 1 1 1 1 

m=8;n=8;base=2;score=92;
1 1 1 1 1 1 0 1 
1 1 0 0 0 0 1 0 
0 0 0 1 0 1 0 1 
1 0 1 0 1 1 0 1 
0 1 0 0 1 0 1 0 
1 0 0 0 1 0 1 0 
1 0 0 0 0 0 1 1 
1 1 1 0 1 1 1 1 

m=8;n=9;base=2;score=119;
1 0 1 1 0 0 0 1 1 
1 1 1 0 0 1 1 0 0 
1 0 0 0 0 0 0 0 1 
0 1 0 1 1 1 0 0 1 
1 1 0 0 0 0 1 0 1 
1 0 1 0 1 0 1 0 0 
0 1 0 1 1 1 1 1 1 
0 1 1 1 1 0 1 1 1 

m=8;n=10;base=2;score=133;
1 1 1 1 1 0 0 0 1 1 
1 1 1 0 0 0 0 0 1 0 
1 0 1 0 1 0 0 1 0 0 
0 1 1 1 1 0 1 1 1 0 
1 0 0 1 0 0 0 0 1 1 
0 1 1 0 1 0 0 0 0 1 
1 0 0 1 0 0 1 1 1 0 
1 1 0 1 1 1 1 1 1 1 

m=9;n=9;base=2;score=135;
1 1 1 0 1 1 1 0 1 
1 1 1 0 1 0 0 1 1 
1 0 0 0 0 1 0 0 1 
1 1 0 0 0 0 0 0 1 
1 0 0 0 0 1 0 1 1 
0 1 0 0 1 0 1 0 1 
0 1 0 0 1 1 1 0 1 
1 1 1 0 1 1 0 1 0 
0 1 1 1 1 0 1 1 1 

m=9;n=10;base=2;score=152;
1 0 1 1 0 0 1 1 1 1 
0 1 1 0 0 0 0 1 0 1 
0 1 0 0 1 0 1 0 1 1 
1 1 1 0 0 1 0 1 1 0 
0 0 1 1 1 0 1 0 1 1 
1 0 0 1 0 0 0 0 1 1 
1 0 1 0 0 0 0 0 0 1 
1 0 0 0 1 1 0 1 1 1 
0 1 1 1 0 1 1 1 0 1 

m=10;n=10;base=2;score=167;
1 1 1 0 1 1 1 1 1 0 
0 1 1 1 1 0 0 1 1 1 
1 1 0 0 1 0 0 1 0 1 
1 0 1 0 0 1 1 1 0 1 
1 0 1 0 0 1 1 0 1 1 
0 0 0 0 0 0 0 0 1 1 
1 0 0 1 1 1 0 0 0 1 
1 1 0 0 0 0 1 1 0 1 
0 0 1 0 1 0 0 1 0 1 
1 1 0 1 0 1 0 1 1 1

base ten:

 x |    1    2    3    4    5    6    7    8    9   10
---+--------------------------------------------------
 1 |    1    2    3    4    5    6    7    8    9   10
 2 |         4    6    8   10   21   32   37   46   54
 3 |              9   26   38   48   66   78   98  104
 4 |                  43   65   88  104  116  125  132
 5 |                       98  108  126  136  149  161
 6 |                           128  141  156  171  182
 7 |                                157  175  191  205
 8 |                                     194  204  234
 9 |                                          236  256
10 |                                               277

m=1;n=1;base=10;score=1;
1 

m=1;n=2;base=10;score=2;
1 2 

m=1;n=3;base=10;score=3;
2 1 3 

m=1;n=4;base=10;score=4;
3 1 4 2 

m=1;n=5;base=10;score=5;
1 3 5 4 2 

m=1;n=6;base=10;score=6;
5 1 4 2 6 3 

m=1;n=7;base=10;score=7;
7 3 2 5 4 6 1 

m=1;n=8;base=10;score=8;
8 7 2 1 5 4 6 3 

m=1;n=9;base=10;score=9;
1 4 6 2 9 5 3 7 8 

m=1;n=10;base=10;score=10;
6 8 7 4 3 1 0 2 5 9 

m=2;n=2;base=10;score=4;
2 3 
1 4 

m=2;n=3;base=10;score=6;
6 5 1 
2 4 3 

m=2;n=4;base=10;score=8;
5 3 1 6 
7 4 8 2 

m=2;n=5;base=10;score=10;
7 5 0 1 4 
9 8 2 3 6 

m=2;n=6;base=10;score=21;
9 1 0 7 4 5 
6 2 8 3 1 1 

m=2;n=7;base=10;score=32;
8 1 0 3 4 2 5 
6 2 1 9 2 1 7 

m=2;n=8;base=10;score=37;
3 1 2 6 3 7 2 8 
4 2 1 0 3 5 1 9 

m=2;n=9;base=10;score=46;
1 7 2 5 4 0 3 2 1 
1 8 3 6 1 4 2 3 9 

m=2;n=10;base=10;score=54;
2 0 1 4 6 3 4 7 3 2 
3 5 4 1 9 2 1 8 2 3 

m=3;n=3;base=10;score=9;
1 9 5 
3 7 4 
6 8 2 

m=3;n=4;base=10;score=26;
9 6 5 2 
8 1 2 3 
7 4 1 0 

m=3;n=5;base=10;score=38;
3 5 4 7 3 
1 3 2 1 6 
1 0 8 2 9 

m=3;n=6;base=10;score=48;
5 3 4 6 2 5 
8 4 0 3 1 2 
1 2 7 1 3 9 

m=3;n=7;base=10;score=66;
1 3 3 7 1 2 5 
6 0 5 4 2 1 8 
2 6 4 5 9 3 4 

m=3;n=8;base=10;score=78;
5 8 2 2 1 4 8 3 
1 5 6 3 0 7 4 9 
9 1 3 6 7 5 2 6 

m=3;n=9;base=10;score=98;
3 4 7 7 9 2 4 8 5 
3 0 4 8 3 5 2 6 5 
6 9 1 1 8 0 1 7 6 

m=3;n=10;base=10;score=104;
8 2 3 9 9 2 2 1 9 7 
6 8 4 6 5 7 0 0 1 8 
6 1 0 4 7 3 3 1 5 5 

m=4;n=4;base=10;score=43;
8 2 5 3 
2 1 0 7 
9 4 1 2 
8 3 3 6 

m=4;n=5;base=10;score=65;
9 2 8 1 1 
5 4 3 5 9 
4 6 7 3 5 
0 1 2 2 0 

m=4;n=6;base=10;score=88;
9 3 0 6 9 1 
2 5 3 4 7 1 
6 1 8 7 4 5 
6 8 0 2 2 5 

m=4;n=7;base=10;score=104;
3 7 6 3 3 1 6 
0 9 2 4 5 8 6 
1 0 4 2 8 5 0 
1 0 1 7 7 9 9 

m=4;n=8;base=10;score=116;
3 3 4 8 6 7 2 4 
5 4 9 0 1 3 7 2 
6 9 1 0 1 0 8 5 
7 6 2 1 1 1 5 8 

m=4;n=9;base=10;score=125;
4 8 6 6 5 1 7 7 4 
5 2 1 0 1 1 0 4 6 
5 7 1 1 0 2 1 3 9 
9 3 8 8 9 1 2 3 9 

m=4;n=10;base=10;score=132;
7 6 1 1 3 1 1 1 1 1 
8 1 0 2 1 3 0 1 2 5 
8 0 1 1 2 4 5 7 6 9 
3 9 9 4 8 5 4 6 7 3 

m=5;n=5;base=10;score=98;
7 7 9 2 3 
5 4 2 5 1 
5 0 6 8 1 
1 7 8 6 9 
4 4 3 3 0 

m=5;n=6;base=10;score=108;
3 1 2 5 6 1 
3 0 5 2 8 0 
1 0 1 7 9 8 
1 0 7 9 3 4 
4 4 6 6 5 2 

m=5;n=7;base=10;score=126;
7 6 1 1 8 8 1 
7 1 2 0 1 4 2 
4 2 1 1 0 9 5 
4 3 0 1 7 8 9 
6 6 5 5 3 3 6 

m=5;n=8;base=10;score=136;
5 6 7 1 3 4 4 7 
4 5 2 3 1 2 0 1 
9 8 1 1 2 1 0 1 
7 8 0 1 3 0 2 0 
7 3 6 6 9 5 9 9 

m=5;n=9;base=10;score=149;
6 6 9 9 8 6 7 9 5 
2 0 1 3 2 1 4 3 1 
1 4 1 2 1 1 0 1 1 
4 2 1 4 0 0 1 3 3 
5 5 7 7 8 8 5 6 1 

m=5;n=10;base=10;score=161;
1 6 7 8 8 5 1 3 7 9 
6 4 3 1 2 6 3 2 4 8 
1 1 5 1 0 1 1 1 4 1 
1 5 0 1 5 3 2 4 0 1 
7 7 6 9 9 2 1 0 8 2 

m=6;n=6;base=10;score=128;
4 7 3 3 4 4 
8 6 0 1 2 0 
6 8 1 1 0 1 
3 5 0 1 2 8 
5 9 2 2 9 6 
4 7 7 1 1 9 

m=6;n=7;base=10;score=141;
5 4 9 1 1 6 9 
4 5 7 0 2 3 9 
8 2 6 3 1 2 8 
1 6 1 4 1 1 8 
0 2 0 1 3 0 7 
0 1 5 3 1 1 7 

m=6;n=8;base=10;score=156;
7 2 1 9 8 1 1 8 
0 3 5 9 3 3 2 8 
3 5 1 4 2 1 0 6 
1 0 1 2 1 1 1 6 
0 4 1 0 5 4 3 7 
7 7 9 6 4 1 8 5 

m=6;n=9;base=10;score=171;
1 3 7 9 9 5 1 2 7 
7 4 3 1 6 0 2 5 7 
1 1 5 1 4 1 1 1 8 
6 5 1 1 2 6 1 4 4 
1 0 3 0 6 3 1 2 9 
8 8 1 1 0 7 1 6 8 

m=6;n=10;base=10;score=182;
1 4 0 1 9 1 8 1 9 9 
6 6 1 3 7 4 6 0 7 8 
1 2 4 4 1 2 1 7 5 3 
8 8 1 1 5 2 1 1 1 1 
2 7 0 6 3 1 0 5 3 2 
1 0 1 1 9 3 6 1 5 9 

m=7;n=7;base=10;score=157;
9 9 7 6 1 4 7 
4 2 8 5 9 3 8 
1 2 4 1 1 0 8 
1 1 1 4 0 1 1 
4 2 3 1 1 5 5 
6 1 0 6 3 2 1 
6 7 7 1 1 3 9 

m=7;n=8;base=10;score=175;
9 1 0 8 1 1 2 9 
3 5 6 1 2 6 4 6 
1 5 1 4 3 1 7 1 
1 3 1 0 1 7 0 9 
5 3 0 1 2 5 1 9 
8 1 6 2 7 1 4 8 
8 6 1 1 4 4 7 1 

m=7;n=9;base=10;score=191;
0 1 0 1 9 1 8 9 9 
1 0 6 7 2 6 5 5 1 
8 8 1 3 1 2 1 7 1 
1 1 4 3 1 1 8 3 1 
1 0 2 1 0 1 5 1 9 
2 5 1 7 4 1 6 4 0 
8 1 6 7 1 6 1 4 1 

m=7;n=10;base=10;score=205;
6 4 7 1 1 3 4 1 2 2 
9 0 1 7 2 4 1 1 0 6 
1 1 5 4 1 5 6 4 2 1 
1 9 7 1 8 6 1 1 9 9 
1 2 8 1 9 1 7 0 6 1 
1 0 0 2 5 3 8 1 3 3 
1 5 2 3 1 5 1 8 1 1 

m=8;n=8;base=10;score=194;
1 3 1 8 5 1 4 7 
0 3 1 3 4 5 5 1 
2 1 6 4 1 1 6 6 
1 2 8 1 0 0 7 1 
1 1 1 3 5 1 6 2 
9 9 4 7 1 9 1 5 
4 3 2 1 8 0 7 1 
1 1 1 1 8 1 7 1 

m=8;n=9;base=10;score=204;
2 1 5 1 8 5 1 0 1 
2 0 4 0 1 6 9 3 8 
6 0 1 9 8 9 7 1 2 
1 2 2 8 1 1 0 5 1 
7 4 1 1 3 3 1 6 1 
1 7 6 9 5 1 4 8 1 
5 6 1 1 2 4 7 1 7 
5 1 6 3 1 1 3 0 2 

m=8;n=10;base=10;score=234;
8 2 2 9 5 1 1 8 1 9 
2 0 8 1 7 4 3 5 4 0 
9 2 1 8 4 1 2 1 0 3 
1 0 7 9 1 2 6 2 2 2 
0 8 1 1 9 3 1 7 0 2 
1 9 6 6 1 2 5 7 1 3 
5 8 1 0 5 4 5 1 3 4 
1 3 3 2 1 1 6 4 0 1 

m=9;n=9;base=10;score=236;
9 6 5 1 5 2 2 6 7 
2 3 2 0 8 1 4 0 1 
2 3 1 1 2 7 1 1 4 
0 1 4 2 1 6 1 9 9 
6 5 6 1 3 1 6 8 1 
1 5 1 2 0 3 9 1 5 
4 7 0 9 1 8 1 7 7 
1 2 0 1 5 8 4 3 1 
8 2 2 2 3 1 4 1 5 

m=9;n=10;base=10;score=256;
1 3 5 6 0 1 2 9 1 8 
1 5 2 0 6 1 3 7 0 2 
2 2 6 3 2 1 9 1 0 2 
7 4 5 2 3 4 1 0 3 1 
1 6 2 0 2 1 7 5 1 6 
1 3 2 4 0 1 1 1 8 4 
5 2 4 1 8 8 6 1 9 1 
9 4 5 2 3 7 1 9 4 7 
1 5 1 2 1 2 1 8 1 7 

m=10;n=10;base=10;score=277;
9 1 1 4 0 5 1 2 0 9 
2 6 5 7 1 9 4 3 6 2 
8 2 2 1 3 5 1 1 3 6 
1 4 4 2 1 2 7 6 2 2 
9 7 1 0 6 7 1 5 5 2 
7 0 8 4 6 1 0 3 7 2 
1 1 1 1 9 1 0 2 7 2 
2 3 8 9 1 8 2 4 2 5 
9 4 8 5 2 6 0 3 0 2 
2 1 6 1 1 2 2 2 0 6

the bonus:

m=20;n=20;base=10;score=1278;
7 5 7 6 7 8 5 8 5 2 1 2 5 7 9 7 1 9 1 5 
8 6 8 6 3 6 0 1 0 8 5 3 1 1 7 4 0 2 1 4 
9 3 8 8 0 7 3 8 7 2 1 1 5 0 1 7 3 7 2 9 
4 2 2 1 0 5 7 0 1 2 8 0 1 0 4 0 3 9 5 1 
8 4 2 1 1 1 4 9 1 1 5 6 1 9 1 1 7 4 0 5 
6 5 2 1 1 1 8 5 9 6 6 0 1 0 0 6 2 2 5 9 
5 2 2 1 9 9 4 9 0 6 6 3 2 1 3 1 1 1 1 4 
3 3 9 3 6 1 8 0 4 2 7 4 0 5 0 8 1 0 7 6 
9 9 7 0 1 2 0 2 4 1 4 2 7 7 8 5 4 8 7 0 
9 8 1 3 1 1 1 9 5 2 0 1 8 4 4 6 4 6 2 1 
8 7 8 1 0 4 3 3 8 7 1 0 1 5 3 4 4 0 0 1 
1 1 0 5 5 9 5 7 3 2 1 2 1 6 0 8 9 8 1 6 
1 2 2 2 0 9 3 7 1 2 0 6 3 1 1 1 0 4 2 4 
6 6 1 1 2 0 0 1 7 1 1 1 3 1 3 0 1 1 4 3 
5 8 4 0 1 1 1 1 1 6 0 1 0 8 1 4 1 1 2 9 
9 8 3 5 0 9 1 0 2 9 2 3 4 9 2 9 5 2 5 7 
3 8 7 9 5 7 8 7 0 6 2 1 9 1 7 6 1 3 3 3 
3 5 6 5 6 9 8 2 9 6 3 5 2 1 6 4 2 2 3 4 
6 9 5 0 2 8 5 7 9 6 2 4 7 6 0 1 0 2 7 3 
9 8 5 1 1 4 7 7 2 1 7 6 5 7 2 1 3 6 1 4