Abstract: | We study difference sets with parameters(v, k, ) = (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. |