Partial difference sets in [formula omitted

Abstract

Let Gn denote the group C2n×C2n, where Ck is the cyclic group of order k. We give an algorithm for enumerating the regular nontrivial partial difference sets (PDS) in Gn. We use our algorithm to obtain all of these PDS in Gn 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 Gn appear to grow super-exponentially in n. For n=9, a typical canonical coloring represents in excess of 10146 group-inequivalent PDS, and there are precisely 2520 reversible Hadamard difference sets.