Reversible and DRAD difference sets in

The existence of Hadamard difference sets has been a central question in design theory. Reversible difference sets have been studied extensively. Dillon gave a method for finding reversible difference sets in groups of the form (C)². DRAD difference sets are a newer concept. Davis and Polhill showed the existence of DRAD difference sets in the same groups as Dillon. This article determines the existence of reversible and DRAD difference sets in groups of the form (C)³. These are the only abelian 2‐groups outside of direct products of C₄ and (C)² known to contain reversible and DRAD difference sets. © 2011 Wiley Periodicals, Inc. J Combin Designs 20:58–67, 2012