Concerning seven and eight mutually orthogonal Latin squares

R. Julian, Charles Colbourn, Charles J. Colbourn, Mieczyslaw Wojtas

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


In this paper, three new direct Mutually Orthogonal Latin Squares (MOLS) constructions are presented for 7 MOLS(24), 7 MOLS(75) and 8 MOLS(36); then using recursive methods, several new constructions for 7 and 8 MOLS are obtained. These reduce the largest value for which 7 MOLS are unknown from 780 to 570, and the largest odd value for which 8 MOLS are unknown from 1935 to 1419.

Original languageEnglish (US)
Pages (from-to)123-131
Number of pages9
JournalJournal of Combinatorial Designs
Issue number2
StatePublished - 2004


  • Difference matrix
  • MOLS
  • Quasi-difference matrix
  • Transversal design

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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