The enumeration of cyclic mutually nearly orthogonal Latin squares


DEMİRKALE F., Donovan D. M. , Kokkala J. I. , Marbach T. G.

JOURNAL OF COMBINATORIAL DESIGNS, vol.27, no.5, pp.265-276, 2019 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 5
  • Publication Date: 2019
  • Doi Number: 10.1002/jcd.21647
  • Journal Name: JOURNAL OF COMBINATORIAL DESIGNS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.265-276

Abstract

In this paper, we study collections of mutually nearly orthogonal Latin squares (MNOLS), which come from a modification of the orthogonality condition for mutually orthogonal Latin squares. In particular, we find the maximum mu such that there exists a set of mu cyclic MNOLS of order n for n <= 18, as well as providing a full enumeration of sets and lists of mu cyclic MNOLS of order n under a variety of equivalences with n <= 18. This resolves in the negative a conjecture that proposed that the maximum mu for which a set of mu cyclic MNOLS of order n exists is left ceiling n/4 right ceiling +1.