Triple arrays from difference sets. Issue 11 (7th August 2017)

• Record Type: Journal Article
• Authors: Nilson, Tomas; Cameron, Peter J.
• Is Part Of: Journal of combinatorial designs. Volume 25:Issue 11(2017:Nov.)
• Page Start: 494
• Page End: 506
• Publication Date: 2017-08-07
• Subjects: block design -- difference set -- triple array -- youden square; Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21569
• Languages: English
• ISSNs: 1063-8539

Abstract

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.