Triple arrays from difference sets
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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.
Nilson , T & Cameron , P J 2017 , ' Triple arrays from difference sets ' , Journal of Combinatorial Designs , vol. 25 , no. 11 , pp. 494-506 . https://doi.org/10.1002/jcd.21569
Journal of Combinatorial Designs
© 2017, Wiley Periodicals Inc. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at onlinelibrary.wiley.com / https://doi.org/10.1002/jcd.21569