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Triple arrays from difference sets

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Nilson_2017_Triple_arrays_JCombinDesign_AAM.pdf (219.3Kb)
Date
11/2017
Author
Nilson, Tomas
Cameron, Peter J.
Keywords
Block design
Difference set
Triple array
Youden square
QA Mathematics
T-NDAS
Metadata
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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.
Citation
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
Publication
Journal of Combinatorial Designs
Status
Peer reviewed
DOI
https://doi.org/10.1002/jcd.21569
ISSN
1063-8539
Type
Journal article
Rights
© 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
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/15775

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