Difference systems of sets (DSS) are combinatorial structures introduced by Levenshtein in (Probl Peredachi Inform 7(3):215-222, 1971), which are a generalization of cyclic difference sets and arise in connection with code synchronization. In this paper, we consider a collection of pairs in a finite field of a prime order to be a regular DSS with parameters . We give a lower bound on the parameter using cyclotomic numbers for and 4. In addition, we present a condition for which the collection of pairs forms an optimal DSS for e = 4.