Triple arrays from difference sets. Issue 11 (7th August 2017) - Nilson, Tomas; Cameron, Peter J.
Abstract: This paper addresses the question of 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 use an alternative version of the construction to analyze 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.