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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Rhodan71
I live in France where I work as a freelance in software development. I support every project but especially astronomic and mathematic ones.

Processing of the square # 51 completed
Dear participants, processing of the square # 51 is fully completed! The square:

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

has 509396858 orthogonal mates which puts it on the 34th place of the rating which include now 5850 positions. Now "high part" of spectra of ODLS-12 looks like this (square # 51 marked by red):


Thank you for project attention, support and donation of CPU time!
11 Dec 2024, 16:28:09 UTC · Discuss

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Processing of the square # 50 completed
Dear participants, processing of the square # 50 is fully completed! The square:

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

has 468979501 orthogonal mates which puts it on the 41th place of the rating which include now 5846 positions. Now "high part" of spectra of ODLS-12 looks like this (square # 50 marked by red):


Thank you for project attention, support and donation of CPU time!
30 Nov 2024, 7:19:37 UTC · Discuss

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Processing of the square # 49 completed
Dear participants, processing of the square # 49 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 0 1 2 9 A B 6 7 8
B A 9 8 7 6 5 4 3 2 1 0
A 9 B 7 6 8 3 5 4 0 2 1
6 8 7 9 B A 1 0 2 4 3 5
4 5 3 1 2 0 B 9 A 8 6 7
9 B A 6 8 7 4 3 5 1 0 2
7 6 8 A 9 B 0 2 1 3 5 4
5 3 4 2 0 1 A B 9 7 8 6
8 7 6 B A 9 2 1 0 5 4 3
2 0 1 5 3 4 7 8 6 A B 9

has 487895876 orthogonal mates which puts it on the 38th place of the rating which include now 5845 positions.

Thank you for project attention, support and donation of CPU time!
30 Nov 2024, 6:55:06 UTC · Discuss

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Processing of the square # 48 completed
Dear participants, processing of the square # 48 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
7 6 B A 9 8 3 2 1 0 5 4
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
8 7 6 B A 9 2 1 0 5 4 3
2 3 4 5 0 1 A B 6 7 8 9

has 497890762 orthogonal mates which puts it on the 37th place of the rating which include now 5827 positions.

Thank you for project attention, support and donation of CPU time!
3 Nov 2024, 9:46:12 UTC · Discuss

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Processing of the square # 47 completed
Dear participants, processing of the square # 47 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 7 9 B 0 3 1 4 2 5
8 A 6 9 B 7 1 4 2 5 0 3
A 6 8 B 7 9 2 5 0 3 1 4
2 0 1 5 3 4 A B 6 7 8 9
5 3 4 1 2 0 B 8 7 A 9 6
4 5 3 0 1 2 9 6 B 8 7 A
B 7 9 8 A 6 5 1 3 2 4 0
9 B 7 6 8 A 4 0 5 1 3 2
7 9 B A 6 8 3 2 4 0 5 1
3 4 5 2 0 1 7 A 9 6 B 8

has 481418765 orthogonal mates which puts it on the 37th place of the rating which include now 5813 positions.

Thank you for project attention, support and donation of CPU time!
3 Nov 2024, 9:44:00 UTC · Discuss

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