Perfect difference systems of sets and the unit group of

A perfect ( v , { | D i | : 0 ≤ i ≤ s − 1 } , ρ ) difference system of sets is a collection of s disjoint subsets D i , 0 ≤ i ≤ s − 1 of Zv, such that every non-zero element of Zv appears exactly ρ times in the multiset { a − b : a ∈ D i , b ∈ D j , 0 ≤ i ≠ j ≤ s − 1 } . In this paper, we give two recursive constructions of perfect DSS s by using the unit group of Z p n , and obtain some infinite classes of perfect DSS s over Z p n .