On the existence of cyclic difference sets with small parameters

Details On the existence of cyclic difference sets with small parameters On the existence of cyclic difference sets with small parameters

2003-04-30

arxiv.org/abs/math/0304502v1

Mathematics

Combinatorics

8 pages. To appear, Proceedings of Fields Institute conference in number theory in honor of Hugh Williams

Scientific paper

Previous surveys by Baumert and Lopez and Sanchez have resolved the existence of cyclic (v,k,lambda) difference sets with k <= 150, except for six open cases. In this paper we show that four of those difference sets do not exist. We also look at the existence of difference sets with k <= 300 and cyclic Hadamard difference sets with v <= 10,000. Finally, we extend an earlier search of the second author to show that no cyclic projective planes exist with non-prime power orders up to two billion.

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