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

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 = Z4, three of the eleven abelian groups of order 64, and 23 of the 256 nonabelian groups of order 64 contain (16, 4, 16, 4) RDSs. If N = Z2 × Z2, six of the abelian groups and 194 of the non-abelian groups of order 64 contain (16, 4, 16, 4) RDSs.