Mutually orthogonal latin squares: A brief survey of constructions

Charles J. Colbourn, Jeffrey H. Dinitz

Research output: Contribution to journalArticlepeer-review

58 Scopus citations


In the two centuries since Euler first asked about mutually orthogonal latin squares, substantial progress has been made. The biggest breakthroughs came in 1960 with the celebrated theorems of Bose, Shrikhande, and Parker, and in 1974 in the research of Wilson. Current efforts have concentrated on refining these approaches, and finding new applications of the substantial theory opened. This paper provides a detailed list of constructions for MOLS, concentrating on the uses of pairwise balanced designs and transversal designs in recursive constructions as pioneered in the papers of Bose, Shrikhande, and Parker. In addition, several new lower bounds for MOLS are given and an up-to-date table of lower bounds for MOLS is provided.

Original languageEnglish (US)
Pages (from-to)9-48
Number of pages40
JournalJournal of Statistical Planning and Inference
Issue number1-2
StatePublished - May 1 2001
Externally publishedYes


  • 05B05
  • 05B15
  • 05B25
  • 51E05
  • 51E10
  • 51E21
  • Block design
  • Mutually orthogonal latin squares
  • Orthogonal array
  • Transversal design

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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