Hi folks!

During the last week in parallel with other searches, a very short experiment was performed in the project. Diagonal Latin square (DLS) with biggest number of transversals (known for us) were passed throws special transformations during which new diagonal Latin squares were obtained and one of them took the lead by number of diagonal transversals - it has 490218 of them, which allowed us to raise value of a(14) member of OEIS A287648 sequence to this value. The found square is:

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

Also this short search allowed to enrich spectra of values of number of diagonal transversals for DLS of 14th order. More information you can read in this message. Thank you for project support, other searches performed immediately now!