1,1

A (v,k,lambda) cyclic difference set is a subset D={d_1,d_2,...,d_k} of the integers modulo v such that {1,2,...,v-1} can each be represented as a difference (d_i-d_j) modulo v in exactly lambda different ways. Difference sets with lambda=1 (planar difference sets) have group order n=k-1. The Prime Power Conjecture states that all abelian planar difference sets have order n a prime power. It is known that shown that no cyclic planar difference sets of nonprime power order n exist with n < 2*10^9 (see Baumert, Gordon link)

Leonard D. Baumert, Daniel M. Gordon, On the existence of cyclic difference sets with small parameters.

Dan Gordon, List of Cyclic Difference Sets

Cf. A095025 number of cyclic difference sets with n elements, A095029-A095047 more examples of cyclic difference set with k=5..20, A000961 prime powers.

Sequence in context: A032849 A038591 A138038 this_sequence A028792 A077459 A048717

Adjacent sequences: A095026 A095027 A095028 this_sequence A095030 A095031 A095032

fini,full,nonn

Hugo Pfoertner (hugo(AT)pfoertner.org), May 27 2004