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 # 32 completed

Dear participants, processing of the square # 32 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 8 A 6 3 2 4 0 5 1

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

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

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

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

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

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

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

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

has 618759046 orthogonal mates which puts it on the 20th place of the rating which include now 5608 positions.

Now "high part" of spectra of ODLS-12 looks like this (square # 32 marked by red):

Thank you for project attention, support and donation of CPU time!

24 Feb 2024, 20:07:57 UTC
· Discuss

Processing of the square # 31 completed

Dear participants, processing of the square # 31 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

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

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

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

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

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

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

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

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

has 27472 diagonal transversals and 1037120685 orthogonal mates, like square # 9. And square #31 can be produced from square #9 by rows permutation, also!

Thank you for project attention, support and donation of CPU time!

15 Feb 2024, 19:16:33 UTC
· Discuss

Project server maintenance 17th January 2024

Dear participants, tomorrow, 2024.01.17 due to server maintenance, the project will stopped for several hours.

Thank you for attention and project participation!

16 Jan 2024, 12:56:40 UTC
· Discuss

Processing of the square # 30 completed

Dear participants, processing of the square # 30 is fully completed! The square:

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

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

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

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

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

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

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

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

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

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

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

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

has 617752973 orthogonal mates which puts it on the 20th place of the rating which include now 5541 positions.

Now "high part" of spectra of ODLS-12 looks like this (square # 30 marked by red):

Thank you for project attention, support and donation of CPU time!

31 Dec 2023, 10:26:15 UTC
· Discuss

Processing of the square # 29 completed

Dear participants, processing of the square # 29 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

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

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

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

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

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

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

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

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

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

has 630001226 orthogonal mates which puts it on the 19th place of the rating which include now 5528 positions.

Now "high part" of spectra of ODLS-12 looks like this (square # 29 marked by red):

Thank you for project attention, support and donation of CPU time!

8 Dec 2023, 22:56:43 UTC
· Discuss

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