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Triple arrays from difference sets
Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics. (Mathematics)ORCID iD: 0000-0003-0930-7116
University of St Andrews, Scotland.
2017 (English)In: Journal of combinatorial designs (Print), ISSN 1063-8539, E-ISSN 1520-6610, Vol. 25, no 11, p. 494-506Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2017. Vol. 25, no 11, p. 494-506
Keywords [en]
Triple array, difference set, Youden square
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-28729DOI: 10.1002/jcd.21569ISI: 000410099000002Scopus ID: 2-s2.0-85029158585OAI: oai:DiVA.org:miun-28729DiVA, id: diva2:963076
Projects
Construction methods for triple arraysAvailable from: 2016-09-07 Created: 2016-09-07 Last updated: 2017-12-18Bibliographically approved

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Publisher's full textScopushttp://onlinelibrary.wiley.com/doi/10.1002/jcd.21569/full

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Nilson, Tomas

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