Relative difference sets suitable for Deza Cayley graph constructions

Construct or identify additional relative difference sets satisfying the parameter conditions in Proposition \ref{rds}, thereby yielding further Deza Cayley graphs over generalized dihedral groups.

Background

Proposition \ref{rds} gives two constructions of Deza Cayley graphs from a nontrivial relative difference set $R$ in an abelian group with a nontrivial forbidden subgroup. The first construction requires $(n,\lambda)=(2,2)$ or $(4,2)$, while the second requires $\lambda=2$.

Lemma \ref{smallrds} supplies several families and examples of relative difference sets meeting these conditions, and Corollary \ref{rdsgraphs} converts them into strictly or non-strictly Deza Cayley graphs. After listing the resulting graphs, the paper states that no further suitable relative difference sets had been found, leaving the search for additional examples unresolved.