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

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

Thank you.
I'll watch it tomorrow.
By the way, I was able to decode DLSs of order 12.

Tomáš Brada
A volunteer performed an interesting experiment using your program.
The results

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

See more here
https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=109&postid=1324

I found a new record for D-transversals in DLS of order 12



This DLS has 28496 D-transversals.
We have for this DLS several million ODLSs.

Tomáš Brada
I run the canonizer

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

The program work 12 hours.
A portion contains 2,715,194 DLS of order 12.

Do I have a chance to get results?

I interrupted the program after 17 hours of work.
Nothing found!

The results that I failed to canonize are posted here
https://yadi.sk/d/P-inaoj1R1rC8A

Read the readme.txt file
See also
https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=109&postid=1333

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

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

Thank you!

This is an interesting result.
I will analyze.

See
https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=109&postid=1343

I calculated and canonicalized orthogonal mates of DaUayP5fWmYHjcNNj3JnBN6rQXiMjg6, but only in path (1994).
https://boinc.tbrada.eu/download/DaUay.1994.kan.txt
There are 179685 ODLK in this fraction, which give 179437 CF ODLK.
Because there are 1994 rows in the first column (30) and I only calculated one, there should be about 360 million ODLK.

Yes, that seems to be the correct prognosis.
My helper's prognosis is ≈ 390 million ODLS.
He found 6.6 million ODLS and then aborted the program.

Can you give my assistant a program that finds the portions of ODLS?

Can you give my assistant a program that finds the portions of ODLS?

It is ortogonbw.exe from this forum.

ortogonbw.exe: (Input) (Path) >output
** Search for Orthogonal mates of Diagonal Latin Square **
Input: encoded diagonal latin square (see dlkconv.exe)
Output: metadata and orthogonal squares in encoded format
Prints to output immediately as square is found. Single thread.
Path: sequence of space-separated numbers narrowing the problem space
Explanation: L(level) c(column) choosen-row / count-rows
Specify number as Path from 1 up to count-rows to narrow down the Search,
specify multiple numbers to narrow down further.
Author: Tomas Brada (GPL)

In this case, 1994 X was used for the path, where X was 1-819, then concatenated the output. Each took about minute and half. To obtain the full solution, the first number would have to go from 1 to 1994.

Thanks, but I didn't understand much.
Is it possible to find all ODLS in this way?

Thanks, but I didn't understand much.
Is it possible to find all ODLS in this way?

Let me write examples... (do not forget space between number 1 and > )

ortogonbw Dv8yEzQnSZSx2gbK2JTvcP6FD7Sh7XQ8 1 >output.txt
init_trans(12) used 495 nodes
num_dtrans: 15928
init_disjoint(12) used 145 heads and 191281 nodes
L(0) c(2) 1 / 198
L(1) c(7) X / 93

This calculates the first part of the problem. It also shows, there are 198 parts. To find all solutions:

ortogonbw Dv8yEzQnSZSx2gbK2JTvcP6FD7Sh7XQ8 2 >>output.txt
ortogonbw Dv8yEzQnSZSx2gbK2JTvcP6FD7Sh7XQ8 3 >>output.txt
ortogonbw Dv8yEzQnSZSx2gbK2JTvcP6FD7Sh7XQ8 4 >>output.txt
...
ortogonbw Dv8yEzQnSZSx2gbK2JTvcP6FD7Sh7XQ8 198 >>output.txt

The output also shows, there are 93 sub-parts to the first part. If it takes too long, it can be split further by adding another number to the command line. Different parts have different number of sub-parts.

Tomáš Brada
Here
https://yadi.sk/d/GnvIaN3dLPEIPg
posted 6640729 CF ODLS for DLS of order 12

DaUayP5fWmYHjcNNj3JnBN6rQXiMjg6

But duplicates of CF ODLS are possible.

Please inform
1. Link for downloading the sort_u program.
2. Instructions for using this program.

Tomáš Brada
I have calculated the number of D-nransversals in DLS of order 20 using your program.

MKWZPV7kaqnWnhbYTFct3gsk15VuhbUvzfGMSTr8fB4tzirPb3jBZuq1HxaeRGTjnpdvsPsAn1jDdb6X8VkLfWFfBJr3cD8pyk5bcCGacY26Ds3qLiMCYSG2
num_dtrans: 23909627000

The program work 19 hours in two threads.

I want to count D-transversals in following DLS of order 20

MNnGrUiv3FCcc7Yjsqjwd3aLxbmTULip8oFYpfv7XbzSmCJagYx94XPkWVTUHfwPhyVZdpKb1K7UmDmkCngSasrtnVofHAF6UGhW1cAkMH94ZWGbDjYB2Qs8QUoeK
MaSWzZ2ebdm5cAneAkniTEZhST67FA1uZGAPN7FCp8a6aq6VsJNFegrB5zdWknjNnrJLzVWrCpcPmMscBDbucW6gQ29RktaVRMrY5JUMTepS7hsa64fKN3ry

Does your program work for order n > 20?

See
https://oeis.org/draft/A287695

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.

Tomáš Brada
Can you arrange to check this result a(12) > = 1764493860?
For this DLS

 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

See
https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=109&postid=1903
Can you guarantee that all ODLS found by your program are different?