Relative (pa, pb, pa, pa-b-Difference Sets: A Unified Exponent Bound and a Local Ring Construction

Abstract

We show that for an odd prime p the exponent of an abelian group of order pa+b containing a relative (pa, pb, pa, pa-b)-difference set cannot exceed p⌊a/2⌋+1. Furthermore, we give a new local ring construction of relative (q2u, q, q2u, q2u-1)-difference sets for prime powers q. Finally, we discuss an important open case concerning the existence of abelian relative (pa, p, pa, pa-1)-difference sets. © 2000 Academic Press.