DLS of orders n = 11 - 22 with known maximum of D-transversals n = 11 4828 D-transversals https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=122&postid=1391 0 1 2 3 4 5 6 7 8 9 10 1 2 3 5 6 9 7 10 0 4 8 7 10 8 0 3 1 5 9 6 2 4 3 5 9 4 10 6 8 0 2 7 1 4 6 7 10 1 8 2 3 9 0 5 5 9 4 6 8 7 0 1 3 10 2 10 8 0 1 5 2 9 4 7 3 6 6 7 10 8 2 0 3 5 4 1 9 8 0 1 2 9 3 4 6 10 5 7 2 3 5 9 7 4 10 8 1 6 0 9 4 6 7 0 10 1 2 5 8 3 n = 12 28496 D-transversals https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=109&postid=1286 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 Properties (utility by Harry White) 1 diagonal Latin 1 associative 1 double axial symmetric 1 natural \diagonal n = 13 131106 D-transversals https://boinc.tbrada.eu/forum_thread.php?id=3104&postid=4133 DLS from complete system MOLS of order 13 0 9 5 1 10 6 2 11 7 3 12 8 4 5 1 10 6 2 11 7 3 12 8 4 0 9 10 6 2 11 7 3 12 8 4 0 9 5 1 2 11 7 3 12 8 4 0 9 5 1 10 6 7 3 12 8 4 0 9 5 1 10 6 2 11 12 8 4 0 9 5 1 10 6 2 11 7 3 4 0 9 5 1 10 6 2 11 7 3 12 8 9 5 1 10 6 2 11 7 3 12 8 4 0 1 10 6 2 11 7 3 12 8 4 0 9 5 6 2 11 7 3 12 8 4 0 9 5 1 10 11 7 3 12 8 4 0 9 5 1 10 6 2 3 12 8 4 0 9 5 1 10 6 2 11 7 8 4 0 9 5 1 10 6 2 11 7 3 12 Properties (utility by Harry White) 1 diagonal Latin 1 associative 1 pandiagonal 1 ultramagic 1 natural \diagonal 1 self-orthogonal n = 14 380718 D-transversals https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=122&postid=1442 0 2 4 12 10 9 8 6 11 7 13 5 3 1 11 1 3 5 8 10 13 12 7 6 4 2 0 9 9 0 2 4 6 7 12 13 10 8 5 3 1 11 7 9 1 3 12 8 5 4 6 13 2 0 11 10 6 7 11 0 4 12 2 3 13 5 1 9 10 8 13 6 10 9 2 5 0 1 4 3 11 7 8 12 1 3 5 13 7 11 6 8 9 10 12 4 2 0 3 4 12 6 9 0 10 7 1 11 8 13 5 2 10 11 0 2 13 6 4 5 8 12 3 1 9 7 2 5 13 8 11 1 7 10 0 9 6 12 4 3 5 12 6 7 0 2 9 11 3 1 10 8 13 4 8 10 9 1 5 13 3 2 12 4 0 11 7 6 4 13 8 10 1 3 11 9 2 0 7 6 12 5 12 8 7 11 3 4 1 0 5 2 9 10 6 13 Properties (utility by Harry White) 1 diagonal Latin 1 axial symmetric 1 natural \diagonal n = 15 389318 D-transversals https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=122&postid=1405 1 14 3 4 5 6 7 9 0 13 12 11 10 2 8 2 3 14 5 6 7 1 11 8 0 13 12 4 10 9 3 4 5 14 7 1 2 13 9 8 0 6 12 11 10 4 5 6 7 14 2 3 8 10 9 1 0 13 12 11 5 6 7 1 2 14 4 10 11 3 9 8 0 13 12 6 7 1 2 3 4 14 12 5 11 10 9 8 0 13 14 1 2 3 4 5 6 0 13 12 11 10 9 8 7 0 9 11 13 8 10 12 14 6 4 2 7 5 3 1 13 0 8 9 10 11 5 4 12 14 3 2 1 7 6 12 13 0 8 9 3 11 2 4 10 14 1 7 6 5 11 12 13 0 1 9 10 7 3 2 8 14 6 5 4 10 11 12 6 0 8 9 5 2 1 7 13 14 4 3 9 10 4 12 13 0 8 3 1 7 6 5 11 14 2 8 2 10 11 12 13 0 1 7 6 5 4 3 9 14 7 8 9 10 11 12 13 6 14 5 4 3 2 1 0 n = 16 32172800 D-transversals https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=122&postid=1408 0 14 4 10 6 8 2 12 13 3 9 7 11 5 15 1 15 1 11 5 9 7 13 3 2 12 6 8 4 10 0 14 6 8 2 12 0 14 4 10 11 5 15 1 13 3 9 7 9 7 13 3 15 1 11 5 4 10 0 14 2 12 6 8 2 12 6 8 4 10 0 14 15 1 11 5 9 7 13 3 13 3 9 7 11 5 15 1 0 14 4 10 6 8 2 12 4 10 0 14 2 12 6 8 9 7 13 3 15 1 11 5 11 5 15 1 13 3 9 7 6 8 2 12 0 14 4 10 5 11 1 15 3 13 7 9 8 6 12 2 14 0 10 4 10 4 14 0 12 2 8 6 7 9 3 13 1 15 5 11 3 13 7 9 5 11 1 15 14 0 10 4 8 6 12 2 12 2 8 6 10 4 14 0 1 15 5 11 7 9 3 13 7 9 3 13 1 15 5 11 10 4 14 0 12 2 8 6 8 6 12 2 14 0 10 4 5 11 1 15 3 13 7 9 1 15 5 11 7 9 3 13 12 2 8 6 10 4 14 0 14 0 10 4 8 6 12 2 3 13 7 9 5 11 1 15 Properties (utility by Harry White) 1 diagonal Latin 1 associative 1 double axial symmetric 1 natural \diagonal 1 self-orthogonal n = 17 204995269 D-transversals https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=122&postid=1409 DLS from complete system MOLS of order 17 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 1 4 5 6 7 8 9 10 11 12 13 14 15 16 0 1 2 3 6 7 8 9 10 11 12 13 14 15 16 0 1 2 3 4 5 8 9 10 11 12 13 14 15 16 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 0 1 2 3 4 5 6 7 8 9 12 13 14 15 16 0 1 2 3 4 5 6 7 8 9 10 11 14 15 16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 1 2 5 6 7 8 9 10 11 12 13 14 15 16 0 1 2 3 4 7 8 9 10 11 12 13 14 15 16 0 1 2 3 4 5 6 9 10 11 12 13 14 15 16 0 1 2 3 4 5 6 7 8 11 12 13 14 15 16 0 1 2 3 4 5 6 7 8 9 10 13 14 15 16 0 1 2 3 4 5 6 7 8 9 10 11 12 15 16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Properties (utility by Harry White) 1 diagonal Latin 1 pandiagonal 1 center symmetric 1 nfr 1 self-orthogonal n = 18 280308432 D-transversals https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=122&postid=1410 1 2 3 4 5 15 7 8 9 0 17 16 6 14 13 12 11 10 4 5 6 7 8 9 1 2 3 12 11 10 0 17 16 15 14 13 7 8 9 10 11 3 4 5 6 15 14 13 12 2 1 0 17 16 8 9 7 2 3 1 5 6 4 13 15 14 10 12 11 16 0 17 2 3 1 5 6 4 17 9 16 7 0 8 13 15 14 10 12 11 5 6 4 8 9 7 2 12 1 10 3 11 16 0 17 13 15 14 6 13 14 9 7 8 3 1 2 11 10 12 17 16 0 5 4 15 0 7 8 3 1 2 6 4 5 14 13 15 11 10 12 17 16 9 3 1 2 6 4 5 9 7 8 17 16 0 14 13 15 11 10 12 17 0 10 11 12 13 14 15 7 16 6 5 4 3 2 1 9 8 14 15 16 17 0 10 11 3 13 4 12 2 1 9 8 7 6 5 11 12 13 14 15 16 8 0 10 1 9 17 7 6 5 4 3 2 13 11 12 16 14 6 10 17 0 9 8 1 15 5 7 3 2 4 10 17 0 13 2 12 16 14 15 6 5 7 3 11 4 9 8 1 16 14 15 1 17 0 13 11 12 3 2 4 9 8 10 6 5 7 15 16 5 0 10 17 12 13 11 2 4 3 8 1 9 14 7 6 12 4 11 15 16 14 0 10 17 8 1 9 5 7 6 2 13 3 9 10 17 12 13 11 15 16 14 5 7 6 2 4 3 8 1 0 Properties (utility by Harry White) 1 diagonal Latin 1 axial symmetric n = 19 11254190082 D-transversals https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=122&postid=1412 DLS from complete system MOLS of order 19 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Properties (utility by Harry White) 1 diagonal Latin 1 pandiagonal 1 center symmetric 1 nfr 1 self-orthogonal n = 20 90010806304 D-transversals https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=122&postid=1471 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2 3 4 0 1 7 8 9 5 6 12 13 14 10 11 17 18 19 15 16 4 0 1 2 3 9 5 6 7 8 14 10 11 12 13 19 15 16 17 18 1 2 3 4 0 6 7 8 9 5 11 12 13 14 10 16 17 18 19 15 3 4 0 1 2 8 9 5 6 7 13 14 10 11 12 18 19 15 16 17 15 16 17 18 19 10 11 12 13 14 5 6 7 8 9 0 1 2 3 4 17 18 19 15 16 12 13 14 10 11 7 8 9 5 6 2 3 4 0 1 19 15 16 17 18 14 10 11 12 13 9 5 6 7 8 4 0 1 2 3 16 17 18 19 15 11 12 13 14 10 6 7 8 9 5 1 2 3 4 0 18 19 15 16 17 13 14 10 11 12 8 9 5 6 7 3 4 0 1 2 5 6 7 8 9 0 1 2 3 4 15 16 17 18 19 10 11 12 13 14 7 8 9 5 6 2 3 4 0 1 17 18 19 15 16 12 13 14 10 11 9 5 6 7 8 4 0 1 2 3 19 15 16 17 18 14 10 11 12 13 6 7 8 9 5 1 2 3 4 0 16 17 18 19 15 11 12 13 14 10 8 9 5 6 7 3 4 0 1 2 18 19 15 16 17 13 14 10 11 12 10 11 12 13 14 15 16 17 18 19 0 1 2 3 4 5 6 7 8 9 12 13 14 10 11 17 18 19 15 16 2 3 4 0 1 7 8 9 5 6 14 10 11 12 13 19 15 16 17 18 4 0 1 2 3 9 5 6 7 8 11 12 13 14 10 16 17 18 19 15 1 2 3 4 0 6 7 8 9 5 13 14 10 11 12 18 19 15 16 17 3 4 0 1 2 8 9 5 6 7 Properties (utility by Harry White) 1 diagonal Latin 1 weakly pandiagonal 1 center symmetric 1 nfr 1 self-orthogonal n = 21 51162162017 D-transversals https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=122&postid=1481 0 12 3 2 17 19 20 18 13 15 16 14 1 8 10 11 9 4 6 7 5 2 1 0 12 20 18 17 19 16 14 13 15 3 11 9 8 10 7 5 4 6 12 3 2 1 18 20 19 17 14 16 15 13 0 9 11 10 8 5 7 6 4 1 0 12 3 19 17 18 20 15 13 14 16 2 10 8 9 11 6 4 5 7 8 10 11 9 4 12 7 6 0 2 3 1 5 17 19 20 18 13 15 16 14 11 9 8 10 6 5 4 12 3 1 0 2 7 20 18 17 19 16 14 13 15 9 11 10 8 12 7 6 5 1 3 2 0 4 18 20 19 17 14 16 15 13 10 8 9 11 5 4 12 7 2 0 1 3 6 19 17 18 20 15 13 14 16 17 19 20 18 13 15 16 14 8 12 11 10 9 4 6 7 5 0 2 3 1 20 18 17 19 16 14 13 15 10 9 8 12 11 7 5 4 6 3 1 0 2 18 20 19 17 14 16 15 13 12 11 10 9 8 5 7 6 4 1 3 2 0 19 17 18 20 15 13 14 16 9 8 12 11 10 6 4 5 7 2 0 1 3 3 2 1 0 7 6 5 4 11 10 9 8 12 16 15 14 13 20 19 18 17 4 6 7 5 0 2 3 1 17 19 20 18 14 13 12 16 15 8 10 11 9 7 5 4 6 3 1 0 2 20 18 17 19 16 15 14 13 12 11 9 8 10 5 7 6 4 1 3 2 0 18 20 19 17 13 12 16 15 14 9 11 10 8 6 4 5 7 2 0 1 3 19 17 18 20 15 14 13 12 16 10 8 9 11 13 15 16 14 8 10 11 9 4 6 7 5 18 0 2 3 1 17 12 20 19 16 14 13 15 11 9 8 10 7 5 4 6 20 3 1 0 2 19 18 17 12 14 16 15 13 9 11 10 8 5 7 6 4 17 1 3 2 0 12 20 19 18 15 13 14 16 10 8 9 11 6 4 5 7 19 2 0 1 3 18 17 12 20 Properties (utility by Harry White) 1 diagonal Latin 1 natural \diagonal 1 self-orthogonal n = 22 3227747329246 D-transversals https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=122&postid=1601 1 13 3 4 5 6 7 8 9 10 11 0 21 20 19 18 17 16 15 14 2 12 2 3 15 5 6 7 8 9 10 11 1 12 0 21 20 19 18 17 16 4 14 13 3 4 5 17 7 8 9 10 11 1 2 13 12 0 21 20 19 18 6 16 15 14 4 5 6 7 19 9 10 11 1 2 3 14 13 12 0 21 20 8 18 17 16 15 5 6 7 8 9 21 11 1 2 3 4 15 14 13 12 0 10 20 19 18 17 16 6 7 8 9 10 11 12 2 3 4 5 16 15 14 13 1 0 21 20 19 18 17 7 8 9 10 11 1 2 14 4 5 6 17 16 15 3 13 12 0 21 20 19 18 8 9 10 11 1 2 3 4 16 6 7 18 17 5 15 14 13 12 0 21 20 19 9 10 11 1 2 3 4 5 6 18 8 19 7 17 16 15 14 13 12 0 21 20 10 11 1 2 3 4 5 6 7 8 20 9 19 18 17 16 15 14 13 12 0 21 0 1 2 3 4 5 6 7 8 9 10 21 20 19 18 17 16 15 14 13 12 11 21 0 12 13 14 15 16 17 18 19 9 20 8 7 6 5 4 3 2 1 11 10 20 21 0 12 13 14 15 16 17 7 19 8 18 6 5 4 3 2 1 11 10 9 19 20 21 0 12 13 14 15 5 17 18 7 6 16 4 3 2 1 11 10 9 8 18 19 20 21 0 12 13 3 15 16 17 6 5 4 14 2 1 11 10 9 8 7 17 18 19 20 21 0 1 13 14 15 16 5 4 3 2 12 11 10 9 8 7 6 16 17 18 19 20 10 0 12 13 14 15 4 3 2 1 11 21 9 8 7 6 5 15 16 17 18 8 20 21 0 12 13 14 3 2 1 11 10 9 19 7 6 5 4 14 15 16 6 18 19 20 21 0 12 13 2 1 11 10 9 8 7 17 5 4 3 13 14 4 16 17 18 19 20 21 0 12 1 11 10 9 8 7 6 5 15 3 2 12 2 14 15 16 17 18 19 20 21 0 11 10 9 8 7 6 5 4 3 13 1 11 12 13 14 15 16 17 18 19 20 21 10 9 8 7 6 5 4 3 2 1 0 Properties (utility by Harry White) 1 diagonal Latin 1 axial symmetric __________________________________________________ Created 17 March 2021