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Enumeration Of (16,4,16,4) Relative Difference Sets, David C. Clark, Vladimir Tonchev

Department of Mathematical Sciences Publications

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 11 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 , nine of the abelian groups and 194 of the non-abelian groups of order 64 contain (16, 4, 16, 4) RDSs.