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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ANCHULA-MARK
A member of the UK Boinc Team supporting SRBase. Apart from computing my interests are reading (mostly old style Sc-Fi), music, countryside walking,...

Processing of the square # 24 completed
Dear participants, processing of the square # 24 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
8 A 6 B 7 9 2 4 0 5 1 3
A 6 8 7 9 B 0 5 1 3 2 4
9 B 7 6 8 A 4 0 5 1 3 2
5 3 4 2 0 1 7 8 9 A B 6
4 5 3 1 2 0 B 6 7 8 9 A
B 7 9 8 A 6 5 1 3 2 4 0
6 8 A 9 B 7 1 3 2 4 0 5
7 9 B A 6 8 3 2 4 0 5 1
3 4 5 0 1 2 9 A B 6 7 8

has 1024457772 orthogonal mates, like square # 23. Square #24 can be produced from #23 by rows permutation, also!

Thank you for project attention, support and donation of CPU time!
11 Sep 2023, 12:09:11 UTC · Discuss

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Processing of the square # 23 completed
Dear participants, processing of the square # 23 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
8 A 6 B 7 9 2 4 0 5 1 3
7 9 B A 6 8 3 2 4 0 5 1
9 B 7 6 8 A 4 0 5 1 3 2
5 3 4 2 0 1 7 8 9 A B 6
A 6 8 7 9 B 0 5 1 3 2 4
B 7 9 8 A 6 5 1 3 2 4 0
6 8 A 9 B 7 1 3 2 4 0 5
4 5 3 1 2 0 B 6 7 8 9 A
3 4 5 0 1 2 9 A B 6 7 8

has 1024457772 orthogonal mates which puts it on the 9th place of the rating which include now 5395 positions.

Now "high part" of spectra of ODLS-12 looks like this (square # 23 marked by red):


Thank you for project attention, support and donation of CPU time!
4 Aug 2023, 20:17:31 UTC · Discuss

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Totals of recent short search, spectra and interesting square of 14th order.
Hi folks!

During the last week in parallel with other searches, a very short experiment was performed in the project. Diagonal Latin square (DLS) with biggest number of transversals (known for us) were passed throws special transformations during which new diagonal Latin squares were obtained and one of them took the lead by number of diagonal transversals - it has 490218 of them, which allowed us to raise value of a(14) member of OEIS A287648 sequence to this value. The found square is:

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

Also this short search allowed to enrich spectra of values of number of diagonal transversals for DLS of 14th order. More information you can read in this message. Thank you for project support, other searches performed immediately now!
16 Jul 2023, 21:00:58 UTC · Discuss

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Processing of the square # 22 completed
Dear participants, processing of the square # 22 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
9 B A 6 8 7 4 3 5 1 0 2
2 0 1 5 3 4 7 8 6 A B 9
7 6 8 9 B A 1 0 2 3 5 4
A 9 B 7 6 8 3 5 4 0 2 1
5 3 4 0 1 2 9 A B 7 8 6
B A 9 8 7 6 5 4 3 2 1 0
8 7 6 A 9 B 0 2 1 5 4 3
3 4 5 1 2 0 B 9 A 6 7 8
6 8 7 B A 9 2 1 0 4 3 5
4 5 3 2 0 1 A B 9 8 6 7

has 1185453085 orthogonal mates, like square # 21 and square # 8. Moreover, as we can see, square # 22 and square # 21 not equal, but one of them can be produced from other by rows permutation. After several years we are again faced with interesting effect of rows permutation! And that is interesting!

Thank you for project attention, support and donation of CPU time!
7 Jul 2023, 19:05:30 UTC · Discuss

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Small bunch of tasks with short deadline
Hello!

In next few days, maybe during 1-2 weeks, the project will send out tasks for search e1067 with short deadline in 1 day. This is necessary for completion of current stage of this search.

Thank you for participation!
2 Jun 2023, 11:17:46 UTC · Discuss

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