Bounds on the maximum number of Latin squares in a mutually quasi-orthogonal set

Bedford, David and Whitaker, Roger Marcus ORCID: https://orcid.org/0000-0002-8473-1913 2001. Bounds on the maximum number of Latin squares in a mutually quasi-orthogonal set. Discrete Mathematics 231 (1-3) , pp. 89-96. 10.1016/S0012-365X(00)00307-1

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Abstract

In this paper we are concerned with finding an upper bound on Nq(n), the maximum number of Latin squares of order n in a mutually quasi-orthogonal set. In doing so, we make use of relationships with orthogonal frequency squares, equidistant permutation arrays and Room squares. We improve upon the best-known bound for Nq(n), n⩾8, by showing that Nq(n)⩽R(n), where R(n) is the maximum number of rows in an equidistant permutation array with n columns and index 1. Much improved bounds are found for special cases.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Uncontrolled Keywords:	Latin square; Quasi-orthogonal; Equidistant permutation array; Room square; Orthogonal frequency square
Publisher:	Elsevier
ISSN:	0012-365X
Last Modified:	18 Oct 2022 13:21
URI:	https://orca.cardiff.ac.uk/id/eprint/13570

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