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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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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Processing of the square # 61 completed
Dear participants, processing of the square # 61 is fully completed! The square:

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

has 25208 diagonal transversals and 493916198 orthogonal mates which puts it on the 39th place of the rating which include now 6028 positions.

Thank you for project attention, support and donation of CPU time!
13 Dec 2025, 20:51:47 UTC · Discuss

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Processing of the square # 60 completed
Dear participants, processing of the square # 60 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
5 0 1 2 3 4 7 8 9 A B 6
8 7 6 B A 9 2 1 0 5 4 3
6 B A 9 8 7 4 3 2 1 0 5
9 8 7 6 B A 1 0 5 4 3 2
3 4 5 0 1 2 9 A B 6 7 8
B A 9 8 7 6 5 4 3 2 1 0
2 3 4 5 0 1 A B 6 7 8 9
A 9 8 7 6 B 0 5 4 3 2 1
7 6 B A 9 8 3 2 1 0 5 4
4 5 0 1 2 3 8 9 A B 6 7

has 25210 diagonal transversals and 469156744 orthogonal mates which puts it on the 47th place of the rating which include now 6027 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 (square # 60 marked by red):


Thank you for project attention, support and donation of CPU time!
20 Sep 2025, 17:01:03 UTC · Discuss

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Processing of the square # 59 completed
Dear participants, processing of the square # 59 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
9 B A 6 8 7 4 3 5 1 0 2
7 6 8 9 B A 1 0 2 3 5 4
A 9 B 7 6 8 3 5 4 0 2 1
B A 9 8 7 6 5 4 3 2 1 0
8 7 6 A 9 B 0 2 1 5 4 3
5 3 4 0 1 2 9 A B 7 8 6
4 5 3 2 0 1 A B 9 8 6 7
2 0 1 5 3 4 7 8 6 A B 9

has 25212 diagonal transversals and 518927416 orthogonal mates which puts it on the 34th place of the rating which include now 6021 positions.

Now "high part" of spectra of ODLS-12 looks like this (square # 59 marked by red):


Thank you for project attention, support and donation of CPU time!
27 Aug 2025, 20:19:14 UTC · Discuss

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