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 # 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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Processing of the square # 64 completed
Dear participants, processing of the square # 63 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
7 6 B A 9 8 3 2 1 0 5 4
2 3 4 5 0 1 A B 6 7 8 9
6 B A 9 8 7 4 3 2 1 0 5
B A 9 8 7 6 5 4 3 2 1 0
9 8 7 6 B A 1 0 5 4 3 2
3 4 5 0 1 2 9 A B 6 7 8
5 0 1 2 3 4 7 8 9 A B 6
A 9 8 7 6 B 0 5 4 3 2 1
8 7 6 B A 9 2 1 0 5 4 3
4 5 0 1 2 3 8 9 A B 6 7

has 25184 diagonal transversals and 465657350 orthogonal mates which puts it on the 53th place of the rating which included at the time of finding 6108 positions.

Thank you for project attention, support and donation of CPU time!
6 May 2026, 6:03:32 UTC · Discuss

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Processing of the square # 63 completed
Dear participants, processing of the square # 63 is fully completed! The square:

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

has 25194 diagonal transversals and 449892030 orthogonal mates which puts it on the 56th place of the rating which included at the time of finding 6078 positions.

Thank you for project attention, support and donation of CPU time!
5 May 2026, 21:53:55 UTC · Discuss

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RakeSearch recovered after technical problems
Dear participants,

thank you for your patience while we were recovering the project. There had been a failure of both SSD discs in a mirror. hoarfrost then did a good job on updating the server and recovering as much data as possible. We had backups of the most important data but not a total backup of everything. I recovered a large part of the forum (sadly excluding the private threads belonging to teams); some particular threads or posts could not be recovered. We hope it does not cause too much inconvenience.

Most of the results you reported before the maintenance have been received, and the credit had been assigned. There may be still some technical glimpses but overall the project is working!

Thank you for participation and the computing power you provide us.

Natalia
4 May 2026, 9:03:32 UTC · Discuss

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Processing of the square # 62 completed
Dear participants, processing of the square # 62 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
6 8 7 B A 9 2 1 0 4 3 5
8 7 6 A 9 B 0 2 1 5 4 3
B A 9 8 7 6 5 4 3 2 1 0
7 6 8 9 B A 1 0 2 3 5 4
9 B A 6 8 7 4 3 5 1 0 2
A 9 B 7 6 8 3 5 4 0 2 1
2 0 1 5 3 4 7 8 6 A B 9
5 3 4 0 1 2 9 A B 7 8 6
4 5 3 2 0 1 A B 9 8 6 7

has 25204 diagonal transversals and 468179486 orthogonal mates which puts it on the 51th place of the rating which include now 6052 positions.

Thank you for project attention, support and donation of CPU time!
24 Dec 2025, 7:48:45 UTC · Discuss

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