Quasi-complete Latin squares: construction and randomization

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A general method for constructing quasi-complete Latin squares based on groups is given. This method leads to a relatively straightforward way of counting the number of inequivalent quasi-complete Latin squares of side at most 9. Randomization of such designs is discussed, and an explicit construction for valid randomization sets of quasi-complete Latin squares whose side is an odd prime power is given. It is shown that, contrary to common belief, randomization using a subset of all possible quasi-complete Latin squares my be valid while that using the whole set is not.
Original languageEnglish
Pages (from-to)323-334
Number of pages12
JournalJournal of the Royal Statistical Society, Series B (Methodological)
Issue number2
Publication statusPublished - 1984


  • complete Latin square
  • complete set of mutually orthogonal Latin squares
  • group
  • quasi-complete Latin square
  • randomization
  • sequenceable group


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