Variations on a Scheme of McFarland for Noncyclic Difference Sets

The k-subset D of the group G of order u is called a (u, k, A, n)-difference set if every nonidentity element of G has exactly 1” representations as a difference of two elements of D; the parameter n is defined to be equal to k I.. Using multiplicative notation for the group operation, we have that D is a difference set precisely when it satisfies in the group ring Z[G] the equation DD'~-"=n l,+%G, (1.1)