Building Symmetric Designs With Building Sets

We introduce a uniform technique for constructing a family of symmetric designs with parameters (v(qm+1-1)/(q-1), kqm,λqm), 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 · 4d, thus obtaining seven infinite families of symmetric designs.

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