dimension 2, word ABBB: 58 tori with at most 30 cells, 6199895886 grids in all
  shape        cells   max ct   max/cell      grids at max   expected
  1x1              1        0   0                       2   not attained  ok
  1x2              2        0   0                       4   not attained  ok
  1x3              3        0   0                       8   not attained  ok
  1x4              4        6   3/2                     4   not attained  ok
  2x2              4        0   0                      16   not attained  ok
  1x5              5        6   6/5                    10   not attained  ok
  1x6              6        6   1                      24   not attained  ok
  2x3              6        4   2/3                    24   not attained  ok
  1x7              7        6   6/7                    56   not attained  ok
  1x8              8       12   3/2                     4   not attained  ok
  2x4              8       12   3/2                     8   not attained  ok
  1x9              9       12   4/3                    18   not attained  ok
  3x3              9        0   0                     512   not attained  ok
  1x10            10       12   6/5                    60   not attained  ok
  2x5             10       12   6/5                    30   not attained  ok
  1x11            11       12   12/11                 176   not attained  ok
  1x12            12       18   3/2                     4   not attained  ok
  2x6             12       12   1                     240   not attained  ok
  3x4             12       18   3/2                     4   not attained  ok
  1x13            13       18   18/13                  26   not attained  ok
  1x14            14       18   9/7                   112   not attained  ok
  2x7             14       16   8/7                    28   not attained  ok
  1x15            15       18   6/5                   400   not attained  ok
  3x5             15       18   6/5                   160   not attained  ok
  1x16            16       24   3/2                     4   not attained  ok
  2x8             16       24   3/2                     8   not attained  ok
  4x4             16       24   3/2                    96   not attained  ok
  1x17            17       24   24/17                  34   not attained  ok
  1x18            18       24   4/3                   180   not attained  ok
  2x9             18       24   4/3                    54   not attained  ok
  3x6             18       18   1                    6540   not attained  ok
  1x19            19       24   24/19                 760   not attained  ok
  1x20            20       30   3/2                     4   not attained  ok
  2x10            20       24   6/5                   660   not attained  ok
  4x5             20       30   3/2                     4   not attained  ok
  1x21            21       30   10/7                   42   not attained  ok
  3x7             21       22   22/21                 609   not attained  ok
  1x22            22       30   15/11                 264   not attained  ok
  2x11            22       28   14/11                  44   not attained  ok
  1x23            23       30   30/23                1288   not attained  ok
  1x24            24       36   3/2                     4   not attained  ok
  2x12            24       36   3/2                     8   not attained  ok
  3x8             24       36   3/2                     4   not attained  ok
  4x6             24       36   3/2                    32   not attained  ok
  1x25            25       36   36/25                  50   not attained  ok
  5x5             25       40   8/5                    10   attained: 10 grids  ok
  1x26            26       36   18/13                 364   not attained  ok
  2x13            26       36   18/13                  78   not attained  ok
  1x27            27       36   4/3                  2016   not attained  ok
  3x9             27       36   4/3                   234   not attained  ok
  1x28            28       42   3/2                     4   not attained  ok
  2x14            28       36   9/7                  1288   not attained  ok
  4x7             28       42   3/2                     4   not attained  ok
  1x29            29       42   42/29                  58   not attained  ok
  1x30            30       42   7/5                   480   not attained  ok
  2x15            30       40   4/3                    60   not attained  ok
  3x10            30       36   6/5                  9330   not attained  ok
  5x6             30       42   7/5                   240   not attained  ok
  violations of the four bounds of Theorem 1.4(a) and 1.1, summed over all tori: [0, 0, 0, 0]
  grids with equality in ct = 8a, 7ct = 12n-4a, 5ct = 12(n-a), 5ct = 8n, summed: [1155, 74, 122, 10]
  tori with a grid on the line 7ct = 12n-4a: ['4x4:64', '5x5:10']
  tori with a grid with a < n on the line 5ct = 12(n-a): ['4x4:64']
  violations of the gap inequality, summed over all tori: 0 ; grids with equality: 10
dimension 3, word ABB: 62 tori with at most 28 cells, 1805645902 grids in all
  shape        cells   max ct   max/cell      grids at max   expected
  1x1x1            1        0   0                       2   not attained  ok
  1x1x2            2        0   0                       4   not attained  ok
  1x1x3            3       18   6                       3   attained: 3 grids  ok
  1x1x4            4       18   9/2                     8   not attained  ok
  1x2x2            4        0   0                      16   not attained  ok
  1x1x5            5       18   18/5                   20   not attained  ok
  1x1x6            6       36   6                       3   attained: 3 grids  ok
  1x2x3            6       36   6                       3   attained: 3 grids  ok
  1x1x7            7       36   36/7                   14   not attained  ok
  1x1x8            8       36   9/2                    48   not attained  ok
  1x2x4            8       36   9/2                    56   not attained  ok
  2x2x2            8        0   0                     256   not attained  ok
  1x1x9            9       54   6                       3   attained: 3 grids  ok
  1x3x3            9       54   6                      12   attained: 12 grids  ok
  1x1x10          10       54   27/5                   20   not attained  ok
  1x2x5           10       48   24/5                   20   not attained  ok
  1x1x11          11       54   54/11                  88   not attained  ok
  1x1x12          12       72   6                       3   attained: 3 grids  ok
  1x2x6           12       72   6                       3   attained: 3 grids  ok
  1x3x4           12       72   6                       3   attained: 3 grids  ok
  2x2x3           12       72   6                       3   attained: 3 grids  ok
  1x1x13          13       72   72/13                  26   not attained  ok
  1x1x14          14       72   36/7                  140   not attained  ok
  1x2x7           14       72   36/7                   56   not attained  ok
  1x1x15          15       90   6                       3   attained: 3 grids  ok
  1x3x5           15       90   6                       3   attained: 3 grids  ok
  1x1x16          16       90   45/8                   32   not attained  ok
  1x2x8           16       72   9/2                  1000   not attained  ok
  1x4x4           16       84   21/4                  432   not attained  ok
  2x2x4           16       72   9/2                  2336   not attained  ok
  1x1x17          17       90   90/17                 204   not attained  ok
  1x1x18          18      108   6                       3   attained: 3 grids  ok
  1x2x9           18      108   6                       3   attained: 3 grids  ok
  1x3x6           18      108   6                      12   attained: 12 grids  ok
  2x3x3           18      108   6                      12   attained: 12 grids  ok
  1x1x19          19      108   108/19                 38   not attained  ok
  1x1x20          20      108   27/5                  280   not attained  ok
  1x2x10          20      108   27/5                   80   not attained  ok
  1x4x5           20      108   27/5                  380   not attained  ok
  2x2x5           20       96   24/5                  160   not attained  ok
  1x1x21          21      126   6                       3   attained: 3 grids  ok
  1x3x7           21      126   6                       3   attained: 3 grids  ok
  1x1x22          22      126   63/11                  44   not attained  ok
  1x2x11          22      108   54/11                1496   not attained  ok
  1x1x23          23      126   126/23                368   not attained  ok
  1x1x24          24      144   6                       3   attained: 3 grids  ok
  1x2x12          24      144   6                       3   attained: 3 grids  ok
  1x3x8           24      144   6                       3   attained: 3 grids  ok
  1x4x6           24      144   6                       3   attained: 3 grids  ok
  2x2x6           24      144   6                       3   attained: 3 grids  ok
  2x3x4           24      144   6                       3   attained: 3 grids  ok
  1x1x25          25      144   144/25                 50   not attained  ok
  1x5x5           25      120   24/5                11905   not attained  ok
  1x1x26          26      144   72/13                 468   not attained  ok
  1x2x13          26      144   72/13                 104   not attained  ok
  1x1x27          27      162   6                       3   attained: 3 grids  ok
  1x3x9           27      162   6                      12   attained: 12 grids  ok
  3x3x3           27      162   6                      39   attained: 39 grids  ok
  1x1x28          28      162   81/14                  56   not attained  ok
  1x2x14          28      144   36/7                 2296   not attained  ok
  1x4x7           28      156   39/7                   56   not attained  ok
  2x2x7           28      144   36/7                  560   not attained  ok
  violations of the gap inequality, summed over all tori: 0 ; grids with equality: 150
RESULT PASS
