A new family of partial difference sets in 3-groups.

In this paper we construct several infinite families of partial difference sets of both the Latin and negative Latin square type. Among these constructions is a new family having parameters (3 2 t , r (3 t + 1) , - n + r 2 + 3 r , r 2 + r) , where r = 3 t - 1 + 1 (new for t ≥ 4 ). For the cases where r = 3 t - 1 - 1 and 3 t - 1 , the constructions generalize previous results to a larger collection of abelian groups. [ABSTRACT FROM AUTHOR]