[RakeSearch] The Square 12/30192/3855983322 finally confirmed!

[BOINC_News]

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!

Source: https://rake.boincfast.ru/rakesearch/fo ... php?id=257