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

Bedford, David and Whitaker, Roger Marcus 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: 04 Jun 2017 02:54
URI: http://orca.cf.ac.uk/id/eprint/13570

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