Small latin squares, quasigroups, and loops

• DOI: 10.1002/jcd.20105
• Publication Date: 2006-03-02T14:46:46Z
• Authors: Brendan D. McKay; Alison Meynert; Wendy Myrvold
• Keywords: Isomorphism (crystallography); Latin square; Quasigroup; Orthogonal array

Abstract We present the numbers of isotopy classes and main Latin squares, isomorphism quasigroups loops, up to order 10. The best previous results were for squares 8 (Kolesova, Lam, Thiel, 1990 ), 6 (Bower, 2000 loops 7 (Brant Mullen, 1985 ). have been independently found by “QSCGZ” Guérin (unpublished, 2001 also report on most extensive search so far a triple mutually orthogonal (MOLS) Our computations show that any such must only with trivial symmetry groups. © 2006 Wiley Periodicals, Inc. J Combin Designs