Five mutually orthogonal latin squares of orders 24 and 40
type: Item
instance of: scholarly article
title: Five mutually orthogonal latin squares of orders 24 and 40
zbMATH Open document ID: 0827.05012
DOI: 10.1016/0012-365X(93)E0173-2
published in: Discrete Mathematics
publication date: 1995-11-27T00:00:00Z
review text: An \((r,n)\)-difference matrix \(D\), over an abelian group \(G\) of order \(n\), is an \(r\times n\) matrix such that the difference of any two distinct rows results in a vector whose set of components equals \(G\). Let \(N(n)\) denote the maximum number of mutually orthogonal latin squares of order \(n\). The existence of an \((r,n)\)-difference matrix implies that \(N(n)\geq r-1\). The author uses a computer to construct \((6,24)\)-difference matrix over \(Z_6 \oplus Z_2 \oplus Z_2\) and \((6,40)\)-difference matrices over \(Z_{10} \oplus Z_2 \oplus Z_2\), thereby establishing that \(N(24)\geq 5\) and \(N(40)\geq 5\).
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 769322
zbMATH Keywords: Hadamard matrix
zbMATH Keywords: difference matrix
zbMATH Keywords: mutually orthogonal latin squares
author: Mieczysław Wojtas
reviewed by: Chester J. Salwach
MaRDI profile type: Publication
cites work: Q4190650
cites work: Four pairwise orthogonal Latin squares of order 24
cites work: Q3829558
description: scientific article; zbMATH DE number 769322