A Sharp Exponent Bound for McFarland Difference Sets withp=2

Abstract

We show that under the self-conjugacy condition a McFarland difference set withp=2 andf≥2 in an abelian groupGcan only exist, if the exponent of the Sylow 2-subgroup does not exceed 4. The method also works for oddp(where the exponent bound ispand is necessary and sufficient), so that we obtain a unified proof of the exponent bounds for McFarland difference sets. We also correct a mistake in the proof of an exponent bound for (320, 88, 24)-difference sets in a previous paper. © 1997 Academic Press.