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Triple arrays from difference sets

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Abstract

This paper addresses the question whether triple arrays can be constructed from Youden squares developed from difference sets. We prove that if the difference set is abelian, then having −1 as multiplier is both a necessary and sufficient condition for the construction to work. Using this, we are able to give a new infinite family of triple arrays. We also give an alternative and more direct version of the construction, leaving out the intermediate step via Youden squares. This is used when we analyse the case of non-abelian difference sets, for which we prove a sufficient condition for giving triple arrays. We do a computer search for such non-abelian difference sets, but have not found any examples satisfying the given condition.
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Original languageEnglish
Pages (from-to)494-506
Number of pages13
JournalJournal of Combinatorial Designs
Volume25
Issue number11
Early online date7 Aug 2017
DOIs
StatePublished - Nov 2017

    Research areas

  • Block design, Difference set, Triple array, Youden square

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