Building Symmetric Designs With Building Sets.

We introduce a uniform technique for constructing a family of symmetric designs with parameters ( v( q ^m+1-1)/(q-1), kq ^m,λ q^m), where m is any positive integer, ( v, k, λ) are parameters of an abelian difference set, and q = k²/( k - λ) is a prime power. We utilize the Davis and Jedwab approach to constructing difference sets to show that our construction works whenever ( v, k, λ) are parameters of a McFarland difference set or its complement, a Spence difference set or its complement, a Davis–Jedwab difference set or its complement, or a Hadamard difference set of order 9 · 4 ^d, thus obtaining seven infinite families of symmetric designs. [ABSTRACT FROM AUTHOR]