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A Unifying Construction For Difference Sets, James A. Davis, Jonathan Jedwab

Department of Math & Statistics Faculty Publications

We present a recursive construction for difference sets which unifies the Hadamard, McFarland, and Spence parameter families and deals with all abelian groups known to contain such difference sets. The construction yields a new family of difference sets with parameters (v, k, λ,n)=(2^2d+4(2^2d+2−1)/3, 2^2d+1(2^2d+3+1)/3, 2^2d+1(2^2d+1+1)/3, 2^4d+2) for d⩾0. The construction establishes that a McFarland difference set exists in an abelian group of order 2^{2 …}