Partial difference sets in C2n×C2n

Abstract Let G n denote the group C 2 n × C 2 n , where C k is the cyclic group of order k . We give an algorithm for enumerating the regular nontrivial partial difference sets (PDS) in G n . We use our algorithm to obtain all of these PDS in G n for 2 ≤ n ≤ 9 , and we obtain partial results for n = 10 and n = 11 . Most of these PDS are new. For n ≤ 4 we also identify group-inequivalent PDS. Our approach involves constructing tree diagrams and canonical colorings of these diagrams. Both the total number and the number of group-inequivalent PDS in G n appear to grow super-exponentially in n . For n = 9 , a typical canonical coloring represents in excess of 1 0 146 group-inequivalent PDS, and there are precisely 2 520 reversible Hadamard difference sets.