  In the present paper, we study relative difference sets (RDSs) and linked
systems of them. It is shown that a closed linked system of RDSs is always
graded by a group. Based on this result, we also define a product of RDS linked
systems sharing the same grading group. Further, we generalize the
Davis-Polhill-Smith construction of a linked system of RDSs. Finally, we
construct new linked system of RDSs in a Heisenberg group over a finite field
and family of RDSs in an extraspecial $p$-group of exponent $p^2$. All
constructions of new RDSs and their linked systems are based essentially on a
usage of cyclotomic Schur rings.
