Sets of partially orthogonal latin squares and projective planes

A. D. Keedwell, G. L. Mullen

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We investigate the construction of sets of t latin squares of a given non-prime-power order q which are as close as possible to being a mutually orthogonal set. The total number of ordered pairs which do not occur when the squares are juxtaposed in pairs will be called the deficiency. Our main result is that complete sets of q - 1 latin squares can be constructed whose deficiency is less than or equal to q(q - 1)2 when q = 10, 12 (that is, it is approximately 18% of the total number of pairs) and sets whose deficiency is less than or equal to 24(q - 1)2 when q = 14, 15.

Original languageEnglish (US)
Pages (from-to)49-60
Number of pages12
JournalDiscrete Mathematics
Volume288
Issue number1-3
DOIs
StatePublished - Nov 28 2004

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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