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A Sharp Exponent Bound for McFarland Difference Sets withp=2
Authors:Siu Lun Ma  Bernhard Schmidt
Institution:aDepartment of Mathematics, National University of Singapore, Kent Ridge, Singapore, 119260, Republic of Singapore;bMathematisches Institut, Universität Augsburg, Universitätsstrasse 15, 86135, Augsburg, Germany
Abstract:We show that under the self-conjugacy condition a McFarland difference set withp=2 andf2 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.
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