Non-existence of partial difference sets in Abelian groups of order 8p3

Document Type

Article

Publication Date

7-7-2018

Department

Department of Mathematical Sciences

Abstract

In this paper we prove non-existence of nontrivial partial difference sets in Abelian groups of order 8p3, where p≥3 is a prime number. These groups seemed to have the potential of admitting at least two infinite families of PDSs, and even the smallest case, p=3 had been open for twenty years until settled recently by the authors and E. Neubert. Here, using the integrality and divisibility conditions for PDSs, we first describe all hypothetical parameter sets of nontrivial partial difference sets in these groups. Then we prove the non-existence of a PDS for each of these hypothetical parameter sets by combining a recent local multiplier result with some geometry and elementary number theory.

Publisher's Statement

© Springer Science+Business Media, LLC, part of Springer Nature 2018. Publisher's version of record: https://doi.org/10.1007/s10623-018-0508-z

Publication Title

Designs, Codes, and Cryptography

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