The enormous size of the diagonal Latin squares space makes it unfeasible to enumerate all its objects straightforwardly in reasonable time. So, in order to discover the structure of this space, sophisticated search methods are needed. In RakeSearch project, we implement an application that picks up separate pairs of mutually orthogonal DLSs, which allows to reconstruct full graphs of their orthogonality.

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Processing of the square # 69 completed
Dear participants, processing of the square # 69 is fully completed! The square:

0 1 2 3 4 5 6 7 8 9 A B
1 2 0 4 5 3 7 A 9 B 6 8
9 B 8 A 6 7 3 4 1 2 5 0
4 5 3 1 2 0 8 9 A 6 B 7
B 8 9 6 7 A 4 5 2 0 3 1
6 7 A B 8 9 1 2 5 3 0 4
2 0 1 5 3 4 A 6 B 8 7 9
5 3 4 2 0 1 9 B 6 7 8 A
7 A 6 8 9 B 2 0 3 4 1 5
A 6 7 9 B 8 0 1 4 5 2 3
8 9 B 7 A 6 5 3 0 1 4 2
3 4 5 0 1 2 B 8 7 A 9 6

has 25152 diagonal transversals and 441679400 orthogonal mates which puts it on the 60th place of the rating which included at the time of finding 6156 positions.

Thank you for project attention, support and donation of CPU time!
7 Aug 2026, 17:52:09 UTC · Discuss

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Processing of the square # 68 completed
Dear participants, processing of the square # 68 is fully completed! The square:

0 1 2 3 4 5 6 7 8 9 A B
1 2 0 4 5 3 8 9 A B 6 7
6 8 A 9 B 7 0 5 1 3 2 4
5 3 4 1 2 0 7 6 9 8 B A
A 6 8 7 9 B 2 4 0 5 1 3
7 9 B 8 A 6 5 0 3 1 4 2
4 5 3 0 1 2 B A 7 6 9 8
3 4 5 2 0 1 9 8 B A 7 6
9 B 7 A 6 8 3 1 4 2 5 0
2 0 1 5 3 4 A B 6 7 8 9
B 7 9 6 8 A 4 2 5 0 3 1
8 A 6 B 7 9 1 3 2 4 0 5

has 25156 diagonal transversals and 445664065 orthogonal mates which puts it on the 58th place of the rating which included at the time of finding 6156 positions.

Thank you for project attention, support and donation of CPU time!
7 Aug 2026, 17:41:52 UTC · Discuss

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Processing of the square # 67 completed
Dear participants, processing of the square # 67 is fully completed! The square:

0 1 2 3 4 5 6 7 8 9 A B
1 2 0 4 5 3 8 6 7 B 9 A
3 4 5 1 2 0 B 9 A 6 7 8
8 7 6 A 9 B 0 2 1 5 4 3
B A 9 8 7 6 5 4 3 2 1 0
A 9 B 7 6 8 3 5 4 0 2 1
7 6 8 9 B A 1 0 2 3 5 4
9 B A 6 8 7 4 3 5 1 0 2
4 5 3 2 0 1 A B 9 8 6 7
6 8 7 B A 9 2 1 0 4 3 5
2 0 1 5 3 4 7 8 6 A B 9
5 3 4 0 1 2 9 A B 7 8 6

has 25164 diagonal transversals and 462533670 orthogonal mates which puts it on the 56th place of the rating which included at the time of finding 6156 positions.

Thank you for project attention, support and donation of CPU time!
7 Aug 2026, 17:33:46 UTC · Discuss

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Processing of the square # 66 completed
Dear participants, processing of the square # 66 is fully completed! The square:

0 1 2 3 4 5 6 7 8 9 A B
1 2 0 4 5 3 7 A B 8 6 9
A 6 7 9 8 B 1 2 4 3 0 5
6 7 A 8 B 9 2 0 5 4 1 3
B 9 8 7 A 6 3 4 0 2 5 1
5 3 4 2 0 1 9 8 A 7 B 6
8 B 9 6 7 A 5 3 2 1 4 0
4 5 3 1 2 0 B 9 7 6 8 A
3 4 5 0 1 2 8 B 6 A 9 7
2 0 1 5 3 4 A 6 9 B 7 8
9 8 B A 6 7 4 5 1 0 3 2
7 A 6 B 9 8 0 1 3 5 2 4

has 25174 diagonal transversals and 501659738 orthogonal mates which puts it on the 39th place of the rating which included at the time of finding 6156 positions.

Thank you for project attention, support and donation of CPU time!
7 Aug 2026, 17:30:03 UTC · Discuss

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Processing of the square # 65 completed
Dear participants, processing of the square # 65 is fully completed! The square:

0 1 2 3 4 5 6 7 8 9 A B
1 2 3 4 5 0 B 6 7 8 9 A
6 B A 9 8 7 4 3 2 1 0 5
4 5 0 1 2 3 8 9 A B 6 7
9 8 7 6 B A 1 0 5 4 3 2
8 7 6 B A 9 2 1 0 5 4 3
5 0 1 2 3 4 7 8 9 A B 6
A 9 8 7 6 B 0 5 4 3 2 1
B A 9 8 7 6 5 4 3 2 1 0
3 4 5 0 1 2 9 A B 6 7 8
2 3 4 5 0 1 A B 6 7 8 9
7 6 B A 9 8 3 2 1 0 5 4

has 25180 diagonal transversals and 513683870 orthogonal mates which puts it on the 35th place of the rating which included at the time of finding 6144 positions. Description and results of other studies can be found on Publications page also.
Now "high part" of spectra of ODLS-12 looks like this (squares # 61 .. 65 marked by magenta):


Thank you for project attention, support and donation of CPU time!
6 May 2026, 8:00:51 UTC · Discuss

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