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.

For account creation please use a **Crunch_4Science** invitation code. It is not needed when registering by BOINC Manager.

Already joined? Log in.

Processing of the square # 18 completed

Dear participants, processing of the square # 18 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

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

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

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

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

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

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

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

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

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

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

has 153240804 orthogonal mates which puts it on the 16th place of the rating which include now 4717 positions. We expected that the smallest number of orthogonal mates would correspond to this square (in comparison to other squares processed in RakeSearch) and now we see that the possible number of orthogonal mates for squares selected for processed in our project lies in the range between hundreds of millions to billions.

Now "high part" of spectra of ODLS-12 looks like this (square # 18 marked by red):

Thank you for participation and donation of CPU Time!

28 Aug 2022, 21:00:45 UTC
· Discuss

Processing of the square # 17 completed

Dear participants, processing of the square # 17 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 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

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 1 3 2 4 0 5

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 1228403532 orthogonal mates which puts it on the 4th place of the rating among another squares with ~1.2 billion mates!

Now "high part" of spectra of ODLS-12 looks like this (square # 17 marked by red):

Thank you for participation and donation of CPU Time!

20 Jul 2022, 17:24:55 UTC
· Discuss

Experiment of calculating the spectra of DLS characteristics

Dear participants!

We start a new joint search with Gerasim@Home project: calculation of spectrum of characteristics of diagonal Latin squares. As mathematical objects, DLS have various numerical characteristics. The spectrum of a characteristic is the range of values it can take. You can read about the scientific background of this new search in presentations of Eduard Vatutin: About Spectra of DLS of small orders and about Spectra of DLS of high orders and volunteer computing grid.

2 Jul 2022, 8:26:26 UTC
· Discuss

Processing of the square # 16 completed

Dear folks, processing of the square # 16 is fully completed also! With you help we know, that the square:

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

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

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

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

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

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

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

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

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

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

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

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

has 575760702 orthogonal mates which puts it on the 13th place of the rating between square with 357535322 orthogonal mates and square with 780235212 mates. And it is interesting!

Thank you for participation and donation of CPU Time!

22 Jun 2022, 11:21:10 UTC
· Discuss

Processing of the square # 15 completed

Dear folks, processing of the square # 15 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

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

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

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

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

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

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

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

has 780235212 orthogonal mates which puts it on the 12th place of the rating. This square is close to square # 14. Another "brick" into the "bridge" between squares with ~ 1 billion orthogonal mates and 300 millions orthogonal mates.

Thank you for participation and donation of CPU Time!

5 Jun 2022, 17:36:03 UTC
· Discuss

... more

News is available as an RSS feed

©2022 The searchers team, Karelian Research Center of the Russian Academy of Sciences