Enumeration of (16,4,16,4) Relative Difference Sets

Abstract

A complete enumeration of relative difference sets (RDS) with parameters $(16,4,16,4)$ in a group of order 64 with a normal subgroup $N$ of order 4 is given. If $N=Z_4$, three of the 11 abelian groups of order 64, and 23 of the 256 nonabelian groups of order 64 contain  $(16,4,16,4)$ RDSs. If $N=Z_2 \times Z_2$, nine of the abelian groups and 194 of the non-abelian groups of order 64 contain  $(16,4,16,4)$  RDSs.