What is RakeSearch?
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 # 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
Processing of the square # 58 completed
Dear participants, processing of the square # 58 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
6 7 A 9 8 B 1 2 5 4 0 3
2 0 1 5 3 4 A 6 9 B 7 8
7 A 6 8 B 9 2 0 3 5 1 4
B 9 8 A 6 7 3 4 1 0 5 2
9 8 B 6 7 A 4 5 2 1 3 0
3 4 5 0 1 2 9 8 7 6 B A
5 3 4 2 0 1 B 9 6 A 8 7
A 6 7 B 9 8 0 1 4 3 2 5
4 5 3 1 2 0 8 B A 7 9 6
8 B 9 7 A 6 5 3 0 2 4 1
has 456623740 orthogonal mates which puts it on the 49th place of the rating which include 6018 positions at the time of publication.
Thank you for project attention, support and donation of CPU time!
27 Aug 2025, 6:46:21 UTC
· Discuss
Processing of the square # 57 completed
Dear participants, processing of the square # 57 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
7 6 B A 9 8 3 2 1 0 5 4
9 8 7 6 B A 1 0 5 4 3 2
B A 9 8 7 6 5 4 3 2 1 0
6 B A 9 8 7 4 3 2 1 0 5
A 9 8 7 6 B 0 5 4 3 2 1
3 4 5 0 1 2 9 A B 6 7 8
2 3 4 5 0 1 A B 6 7 8 9
4 5 0 1 2 3 8 9 A B 6 7
has 480000676 orthogonal mates which puts it on the 44th place of the rating which include 6018 positions at the time of publication.
Thank you for project attention, support and donation of CPU time!
26 Aug 2025, 9:01:40 UTC
· Discuss
Processing of the square # 56 completed
Dear participants, processing of the square # 56 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
2 0 1 5 3 4 A B 6 7 8 9
B 7 9 6 8 A 5 0 3 1 4 2
A 6 8 7 9 B 0 5 1 3 2 4
9 B 7 A 6 8 4 2 5 0 3 1
5 3 4 1 2 0 7 6 9 8 B A
4 5 3 0 1 2 B A 7 6 9 8
3 4 5 2 0 1 9 8 B A 7 6
6 8 A 9 B 7 1 3 2 4 0 5
7 9 B 8 A 6 3 1 4 2 5 0
8 A 6 B 7 9 2 4 0 5 1 3
has 468362488 orthogonal mates which puts it on the 48th place of the rating which include 6018 positions at the time of publication.
Thank you for project attention, support and donation of CPU time!
24 Aug 2025, 19:28:25 UTC
· Discuss
Processing of the square # 55 completed
Dear participants, processing of the square # 55 is fully completed! The square:
0 1 2 3 4 5 6 7 8 9 A B
1 2 0 4 7 8 9 3 A B 5 6
A 5 8 6 9 2 4 B 0 7 1 3
7 3 4 1 2 6 5 0 9 8 B A
5 8 A 9 B 0 7 6 1 3 2 4
6 9 B 8 A 7 0 5 3 1 4 2
8 A 5 B 6 1 3 9 2 4 0 7
B 6 9 5 8 4 2 A 7 0 3 1
9 B 6 A 5 3 1 8 4 2 7 0
4 7 3 0 1 B A 2 6 5 9 8
3 4 7 2 0 9 8 1 B A 6 5
2 0 1 7 3 A B 4 5 6 8 9
has 468362488 orthogonal mates which puts it on the 46th place of the rating which include now 6005 positions.
Thank you for project attention, support and donation of CPU time!
11 Jul 2025, 5:36:52 UTC
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©2025 The searchers team, Karelian Research Center of the Russian Academy of Sciences