Dear participants!

As previously announced (Ru), on August 18, 2021, as part of a separate computational experiment (which did not require calculations in the desktop grid, but is a separate interesting task) Eduard Vatutin found a very interesting diagonal Latin square of order 12 with 30192 diagonal transverses:

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

This number of transverses was a record (and is so at the moment), which suggested that this square may be accompanied by many orthogonal diagonal Latin squares (ODLS). Search were launched in the Gerasim@Home project, which ended on October 24, 2021 (Ru), issued a record value of the ODLS, but the results obtained were questioned by the authors and declared preliminary, since during processing 7 out of 1214514 results corresponding to one of the 30192 transverses suffered due to a failure in one of the memory banks (which was then replaced). Recomputing of 480 workunits from the "broken" 1421 transversal (Ru) was executed very quickly and by October 27, a new, slightly larger value was already known.
But the following questions remain:
1) How reliable are the calculations performed in grids from a PC? (It is raised at every conference dedicated to supercomputing and grid technologies);
2) The fact that 7 corrupted results were found did not mean that there were only 7 of them;
3) When we talk about calculating this characteristic (as well as many other integer ones), it is important for us to get an absolutely accurate value, even +/- 1 - it will already be incorrect;
4) The project Gerasim@Home is a independent development by SerVal, that compatible with BOINC infrastructure through support of BOINC protocol, but still is not "original BOINC server".
Taking into account the above, the decision was made to perform a complete recomputing for this square in the project Gerasim@Home and two weeks later, on November 5 in RakeSearch project.

On November 11, a sudden help came - information appeared (Ru) that one of the active participants of distributed computing from the Russia Team - CoolAtchOk, using programs based on the algorithm of Alexey Belyshev (whitefox), processed the square of Eduard, obtained a value that coincides with that obtained as a result of recalculation on October 24 - 27.

And today, on the 15th of December, 2021, after conducting a full check in RakeSearch and Gerasim@Home projects, we can confidently say that:
1. The number of ODLS for this record (at the moment) square is 3855983322, which coincides with the values obtained after recalculation of the 1421st transversal and the CoolAtchOk participant;
2. Calculations in PC-based grids are really reliable due to the quorum and we have another "hard argument" to such a question.

What's next? Now the last hundreds of tasks for another square are being counted (square # 5), and the result may be close to a record, also the processing of another one (square # 6) is in full thrust!

Thank you for participation and donation of CPU time!

Excellent news.

Michael.

---

President of Rechenkraft.net.
Fördern, kooperieren und konstruieren statt fordern, konkurrieren und konsumieren.

Hello!

On November 11, a sudden help came - information appeared (Ru) that one of the active participants of distributed computing from the Russia Team - CoolAtchOk, using programs based on the algorithm of Alexey Belyshev (whitefox), processed the square of Eduard, obtained a value that coincides with that obtained as a result of recalculation on October 24 - 27.

I want to add that this was an independent experiment as part of my manual project to investigate the properties of ODLS of order 12.
CoolAtchOk is the technical executor of this experiment.
He helped me with many technical calculations.

See
https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=133&postid=3218

The resulting record result was entered into the OEIS on November 11 of this year, as soon as it was obtained by CoolAtchOk in this experiment.
http://oeis.org/A287695

a(12) >= 3855983322. The result belongs to DLS, which has 30192 diagonal transversals. Calculations performed by a volunteer. - Natalia Makarova, Tomáš Brada, Nov 11 2021

The experiment used the Tomáš Brada program (ODLS search in parts).
As shown by this experiment and a similar previous experiment, this program is very effective.

It is also important to note that in my experiment all ODLS are found and published here
https://disk.yandex.ru/d/9qa_dvLbM6MJlw
These ODLS can be used for further research.

I can only write about what I know for sure. It is listed in first message and I can repeat it with a few additions.
- The square (about we talk) was discovered by Eduard Vatutin on August 18, 2021.
- Starting from August 26, 2021, the Gerasim@Home project began processing it and the square itself became freely accessible due to the fact that it can be easy read from each of 1.2 million workunits. Starting from this date, I have no opportunity to call other declarations of this square as discoveries.
- After 3 days of recomputing of 480 workunits from 24 October, 2021 until 27 October, Eduard informs me and other colleagues about results of recomputations and obtaining a new value.
- November 11, 2021. The result obtained by CoolAtchOk coincided with the data, obtained by October 27 and thanks to his work with machines, we now have another confirmation of the result (Gerasim@Home, CoolAtchOk, RakeSearch).

I repeat: I gave an explanation of my experiment here
https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=133&postid=3218

- Starting from August 26, 2021, the Gerasim@Home project began processing it and the square itself became freely accessible due to the fact that it can be easy read from each of 1.2 million workunits. Starting from this date, I have no opportunity to call other declarations of this square as discoveries.

The appearance of a square of 1.2 million workunits is not an official publication.
The square was officially published by Vatutin in the OEIS on September 27, 2021.
The square was also independently found by me and published on the forum on September 27, 2021.
https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=138&postid=3056
(You can compare the time of these publications).
I am not announcing this as my discovery.
The square was found and on October 1, 2021, an experiment was launched to search for ODLS to this DLS.
It was an independent experiment.