On New Families of Supplementary Difference Sets over Rings with Short Orbits

We discuss difference sets (DS) and supplementary difference sets (SDS) over rings. We survey some constructions of SDS over Galois rings where there are no short orbits. ,From there we move to constructions which involve short orbits. These give rise to new infinite families of SDS over GF(p) x GF(q), p, q both prime powers. Many of these families have λ = 1. We also show some new balanced incomplete block designs and pairwise balanced designs arising from the constructions given here.