  Recently, new combinatorial structures called disjoint partial difference
families (DPDFs) and external partial difference families (EPDFs) were
introduced, which simultaneously generalize partial difference sets, disjoint
difference families and external difference families, and have applications in
information security. So far, all known construction methods have used
cyclotomy in finite fields. We present the first non-cyclotomic infinite
families of DPDFs which are also EPDFs, in structures other than finite fields
(in particular cyclic groups and non-abelian groups). As well as direct
constructions, we present an approach to constructing DPDFs/EPDFs using
relative difference sets (RDSs); as part of this, we demonstrate how the
well-known RDS result of Bose extends to a very natural construction for DPDFs
and EPDFs.

Combinatorics