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 # 38 completed

Dear participants, processing of the square # 38 is fully completed! The square:

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

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

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

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

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

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

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

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

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

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

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

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

has 541571814 orthogonal mates which puts it on the 26th place of the rating which include now 5711 positions.

Now "high part" of spectra of ODLS-12 looks like this (square # 38 marked by red):

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

17 May 2024, 19:35:50 UTC
· Discuss

Processing of the square # 37 completed

Dear participants, processing of the square # 37 is fully completed! The square:

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

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

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

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

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

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

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

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

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

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

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

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

has 527873490 orthogonal mates which puts it on the 28th place of the rating which include now 5684 positions.

Now "high part" of spectra of ODLS-12 looks like this (square # 37 marked by red):

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

17 May 2024, 19:33:31 UTC
· Discuss

Processing of the square # 36 completed

Dear participants, processing of the square # 36 is fully completed! The square:

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

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

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

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

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

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

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

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

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

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

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

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

has 575323340 orthogonal mates which puts it on the 24th place of the rating which include now 5678 positions.

Now "high part" of spectra of ODLS-12 looks like this (square # 36 marked by red):

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

11 Apr 2024, 15:00:24 UTC
· Discuss

Processing of the square # 35 completed

Dear participants, processing of the square # 35 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 0 1 2 9 8 B A 7 6

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

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

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

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

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

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

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

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

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

has 549717331 orthogonal mates which puts it on the 24th place of the rating which include now 5665 positions.

Now "high part" of spectra of ODLS-12 looks like this (square # 35 marked by red):

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

11 Apr 2024, 14:57:52 UTC
· Discuss

Processing of the square # 34 completed

Dear participants, processing of the square # 34 is fully completed! The square:

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

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

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

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

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

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

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

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

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

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

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

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

has 610170218 orthogonal mates which puts it on the 22th place of the rating which include now 5651 positions.

Now "high part" of spectra of ODLS-12 looks like this (square # 34 marked by red):

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

21 Mar 2024, 7:22:07 UTC
· Discuss

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©2024 The searchers team, Karelian Research Center of the Russian Academy of Sciences