Abstract
We study difference sets with parameters(v, k, λ) = (p s(r 2m - 1)/(r - 1), p s-1 r 2m-2 r - 1)r 2m -2, where r = r s - 1)/(p - 1) and p is a prime. Examples for such difference sets are known from a construction of McFarland which works for m = 1 and all p,s. We will prove a structural theorem on difference sets with the above parameters; it will include the result, that under the self-conjugacy assumption McFarland's construction yields all difference sets in the underlying groups. We also show that no abelian .160; 54; 18/-difference set exists. Finally, we give a new nonexistence prove of (189, 48, 12)-difference sets in Z 3 × Z 9 × Z 7.
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Ma, S.L., Schmidt, B. Difference Sets Corresponding to a Class of Symmetric Designs. Designs, Codes and Cryptography 10, 223–236 (1997). https://doi.org/10.1023/A:1008200605620
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DOI: https://doi.org/10.1023/A:1008200605620