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Small Latin Squares, Quasigroups and Loops

McKay, Brendan; Meynert, Alison; Myrvold, Wendy


We present the numbers of isotopy classes and main classes of Latin squares, and the numbers of isomorphism classes of quasigroups and loops, up to order 10. The best previous results were for Latin squares of order 8 (Kolesova, Lam, and Thiel, 1990), quasigroups of order 6 (Bower, 2000), and loops of order 7 (Brant and Mullen, 1985). The loops of order 8 have been independently found by "QSCGZ" and Guérin (unpublished, 2001). We also report on the most extensive search so far for a triple of...[Show more]

CollectionsANU Research Publications
Date published: 2007
Type: Journal article
Source: Journal of Combinatorial Designs
DOI: 10.1002/jcd.20105


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