SM6rf4CCPzyjoDCpiCwYTtpZfZK4Vfh2gHmsatksajrv4a55xPQ2DEYXMmWPbzU8rAEt4uAcBa8xqHTnJGCzgbhZJroRQFYUF3xSU94XpfSRZfr27EmhqqsLyRjhmRzw7zUehCp8FCdVts2RvY3deRUPac1XmKea4oojEZJq4RFpgvYkJEUpW5evFfoLW1kivZxRMTjKPZxiiX9zgVLjPLqSzjtp6jdyBXo8gfcqA1s4
SH4HjzTqB1HNkL9amheGCYeCatL9PQEqeZ1YoTbvTdUpjq8dahYsWTqGwYZRotEkEh97NuqmaqRsgvth4f76gP3YRsHUUJH8eGDp5xurfz4yMxantMWsW8VDBJnK2vEjsoUK6dRTdpB6pnvnHhbpjAeYQgvR7N6JZGTg5tMscS31tFuR3R3sdq9pQrF4gnQ3XCGBGXvPyBNTkoiJ5LNirGLRf2i1A8z4
SKN5wh17uYik9jnKyuicaFf5eQZ3bUA1Hwktpa4WLLnTnpmdXbDwamnjg38a8Lgxhi1mGMwSVh3pwU4rgnVSMve4ND3rGDHTwKScve8yFEGG7ci3YRT2ZGK2j8DfgNJL5vZjcJaX37AwooXqs1RAgkTc1HVuWPeAoeKnRuD1WwhPKR2CYQqw3cKsvVGkVKmcBJKSPQpB3pPbjFyfxavTdjJY3g4JHCjTXcPpZ6CJVQamYnkmSdu3
S3U5nuw43PCBnbNWm219vYXWRSxq5DocL8qURcpfggu97GLjeJQAF84HeSYr4nkV6Lq7ByD15k33RdiQtbiTq41u6m24ootQ2aLHfvZ2cz3sSePkDZ79cdQiKd7rfTx3rBwPt4NubaCeq8DsxW6h7h1uXZ6ySpU21JcPony7GsRDyyMykGVAysgZuSwL5mnBKUQPNZdK6VWvzgF555U2wZQGhqswdrXVVbErs5ECCZBj
SRLyrRaBpEZD1gbKZyj2C1ZyPJXBF7hYqp7EfHzNraEv6EZAHjGf7N5B4CPA1taD7sbxn7RNRDXLtX221AUUogVnvhYiey6wj69LG5wSFyVLaYHuuBKXnaukNJKGa7jsi9gy9J318tL3BJ4KqEb2cWRCpwQyofM5sGyayyuSY1Vz2FpH114pgn4AKgWZf
SW1WHkz5Lotr34AiW7d3xU569Xrsp6FFQLn7Deqm3LddYoXNUWuhBCLENNTN88wGXqu4coTXQewn84UdNgkZxUAXfEbD4QjrodEPm99hzjRkYTJxAp18qxZkEC2XxTxDRascgG2EnMxxSWuonq913AGYBbT4vXB2mnfC8ogBYjgcazF82XCCYEMNEEiYHWqyiPezPjuW92d3R2oc6iqYSjMqhwiz7qGGW8kiePkrxhLxc3wHA9DYUAv
SiksCKHqMKTDTEBRx786r25pHMqr8v9QSKNP3Qcox9zyzcpwjPiugrPWHiJGhX5bX3fcrSPX5t24wSPbDWRG8DGWAVJZkfvqTkm91sxg7wZEyPF5hg7cPxGU9vU19jGSWmxehtmWA3PN5DXnp2nnbNJHtSwrnmqEdKurDNwsiRnPWSVadioy9hw9HYcvTSBGAPBFZaup63N6fRjN
SpsXFMwBfwHwUTVofhMsBXtyzLnaJoXmjsS27hXyPrQyRzrmt4k9aeLMXFkTDDuyutpa8bpiBic3y6jPmJx2dJdBZYogKC1XL4KQNDVE9kCSw1iF5MBsopRXdRNGcgMzCVVSJFxLgPm5bVAojRyHFFwKsJRXbyTGV5jcWpVxMnojXF33T8DNLRYy5ok8z
SctDVd8qQFgDY8MMZbAV4zGtWDuu3qwuBwzn7P1xm2n23P7ba374HuRsbT9rK9ebbkk6TRvE5jATdCe4Tihcxb9Y1gTafUUmad4DX18vxErhj9HrQnh7q3KWH5JafsUAshtk99k2eDMnqgshaAVvfyuRa5TpWvXEUAR2ZR496CTznc9xwT3M7fJTgWq4SgBPgHcn9szqfuzejoKYECaC95TGFPRe3KR9h2
SUnoyXJETF8BaVPeg9Xs6MWvRF1y96diSjefiwyDVS8YAMSPrgqf8g4zpcNyVhXG9bm4zCkmzgYfjwJaXMU2sJwyhdiuYdnVLRpfCy19V5Hq9zx26PtyqaUjrC2qptMHuYJR5oAR8CvHHuc4sQnqk6m9ogZKH3EABoJnr9eMBxtfmcWxFiAxrHyCiNQtpbHbrhDjMwovXLxGN7jF

A big motivation loss was that OEIS does not accept any more sequences to prime tuples, however, I did not realize, extensions to existing sequences are still accepted.

Thu Apr 29 08:36 Eduard I. Vatutin: As far as I know, the calculation of the ODLS number for the DLS of order of 12 was carried out by separate parts (subtasks). Natalia, can you guarantee that there are no repeating ODLSs in the separate parts? This requires the use of a number of special algorithmic techniques. Otherwise, the estimate 1764493860 is significantly overestimated.
08:50 Natalia Makarova: Yes, all ODLS are different. They may be isomorphic, but not the same. My assistant has all the results. You can check them if in doubt. No special techniques are required for this. I started posting results here https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=109&postid=1907
Fri Apr 30 07:40 Joerg Arndt: If 1764493860 is too big than the inequality a(12) >= 1764493860 could be plain wrong!
07:42 Joerg Arndt: Eduard shall decide whether the edit is OK or not.
08:59 Eduard I. Vatutin: Joerg, I plan to recheck this result in near future, but this requies some amount of computing time, maybe some weeks... My best result for this value is 4167043 for this moment, see https://vk.com/wall162891802_1660, but computing experiment still going and this border can change in the near future. Now I do not want to add my intermediate result a(12)>= 4167043 for this reason, I propose to wait until the end of the calculations. The resulting value looks too large, but on the other hand, the square has a large number of diagonal transversals (my best square for this moment has 15456 diagonal transversals, Natalia's square — 28496). IMHO we needs independent confirmation of this value due to my distributed implementation of the DLX algorithm has special feature which guarantees the absence of duplicates in various subtasks (in Russian briefly see here: https://vk.com/wall162891802_1650). Implementation of Tomas Brada (according to Natalia's answer) does not have this feature, which causes mistrust. I cannot say that it is wrong, but it must be rechecked...
09:07 Eduard I. Vatutin: Is there a description of the DLX parallelization strategy anywhere? It is unclear to me how to break the coverage matrix with 28496x144 size into 2048 = 2^11 subtasks. Has the developed software implementation been tested on other known examples of squares with known number of orthogonal mates?
11:47 Natalia Makarova: “If 1764493860 is too big than the inequality a(12) >= 1764493860 could be plain wrong!” This is a strange statement! All results are available. My computer is unable to test a 40 GB array of solutions. Take the results from here https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=109&postid=1907 and check the solutions for a match. If you find the same ODLS, show them. Then you can say that the result is wrong. I will continue to publish the results. A total of 21 archives with a volume of about 40 GB. The Tomáš Brada program has been tested many times in calculations. There is no reason to say that she gave the wrong result. In principle, there cannot be identical ODLS. I checked the results of two parts. The first part is 694221 ODLS, the second part is 673322 ODLS. This batch of solutions does not have the same ODLS. This is very easy to verify. Judging by the post of Eduard I. Vatutin, he does not yet know how to check the result a (12)> = 1764493860. Let someone check it out who knows how to check this. While I am changing the value: a (12) > 6640729. See post https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=109&postid=1359. This result was found by the program Belyshev and checked on my computer. Belyshev’s program works on a different principle, it cannot issue the same ODLS. I am sure that the result a (12) > = 1764493860 is correct, but I am not able to check all these squares for a match.

 0 10  4  6  2  8  9  3  7  5 11  1
11  1  7  5  9  3  2  8  4  6  0 10
 4  6  2  8  1 11 10  0  9  3  7  5
 7  5  9  3 10  0  1 11  2  8  4  6
 3  9  0 10  4  6  7  5 11  1  8  2
 8  2 11  1  7  5  4  6  0 10  3  9
 2  8  1 11  5  7  6  4 10  0  9  3
 9  3 10  0  6  4  5  7  1 11  2  8
 5  7  3  9  0 10 11  1  8  2  6  4
 6  4  8  2 11  1  0 10  3  9  5  7
 1 11  5  7  3  9  8  2  6  4 10  0
10  0  6  4  8  2  3  9  5  7  1 11

I promise the project will resume sending spt work 12.06.2021 (June 12th).

I already have a more powerful replacement ordered, just it is stuck in customs for a month already.

See other rare tuples and their contributors here: https://hr.tbrada.eu/tomas/spt_explore.php?rare

MKWZPV7kaqnWnhbYTFct3gsk15VuhbUvzfGMSTr8fB4tzirPb3jBZuq1HxaeRGTjnpdvsPsAn1jDdb6X8VkLfWFfBJr3cD8pyk5bcCGacY26Ds3qLiMCYSG2
num_dtrans: 23909627000

MNnGrUiv3FCcc7Yjsqjwd3aLxbmTULip8oFYpfv7XbzSmCJagYx94XPkWVTUHfwPhyVZdpKb1K7UmDmkCngSasrtnVofHAF6UGhW1cAkMH94ZWGbDjYB2Qs8QUoeK
MaSWzZ2ebdm5cAneAkniTEZhST67FA1uZGAPN7FCp8a6aq6VsJNFegrB5zdWknjNnrJLzVWrCpcPmMscBDbucW6gQ29RktaVRMrY5JUMTepS7hsa64fKN3ry

DaUayP5fWmYHjcNNj3JnBN6rQXiMjg6

I canonicalized 2715194 mates of Dv8yEzQnSZSx2gbK2JTvcP6FD7Sh7XQ8, in parts.
Used a split program to split the file into 5 parts, then ran kanonb on each, then ran sort -u on all of them to obtain 1074993 CF ODLK.
https://boinc.tbrada.eu/download/Dv8yEzQnSZSx2gbK2JTvcP6FD7Sh7XQ8.kan.txt

C:\Users\Дом\Downloads\ndlk-2101b>kanonb.exe -u  0<out.txt 1>output.txt
# KanonizerV: read kanonb_cache_12.dat: 12 21 23040 552960

# in: Dv8yEzQnSZSx2gbK2JTvcP6FD7Sh7XQ8
# num_dtrans: 15928
# num_mates: 2715194
DFcaRhr2tq39qe2KWD3JdJ6iHjsMYr3
DXotD9kYUxycr4Hfkb4F5SkW45LmPRp2
DzVVMrvvFgm4mBMaAHxeXq71JJFonLG
DCHMKAVYUsaiig9Xx6M6b4s19whfipE5
DHHsjeRRMYxP2GM46VZF71zQ2dPBV42
DnQHbaU329cbLyvJyCsRCLFCmVWJizPV
D19HdBLAWiY6L2YC6SemV4qPTRLnce
DRR9Ys1mi8YB3Te3sfcVYqZbR7e1edx4
DRWzuJBDxvh56g4oDK5UZzpG1p9NDae4
D3sRWjKQSvEUgjkHuc5TvtAWP97fzR8
D8SCTvb5WdFyGDsNWwcEtYNrvPB6RhH3
. . . . . 

Natalia Makarova
I changed some things in the programs, please try it and let me know if there are issues.

Download windows build b1b4dc24f04:
https://boinc.tbrada.eu/download/ndlk-2101b.zip
* changed way encoded dlk is read in dlkconv, hopefully fixing crash on windows
* improved speed of transversal counting ortogonb.exe -c
* add kanonb -u mode, unique and sorted output
* small change to ortogonbw output