There Exists a Simple Non Trivial t-design with an Arbitrarily Large Automorphism Group for Every t

In 1987, Teirlinck proved that if t and v are two integers such that v ≡ t (mod(t + 1)!(2t+1)) and v ≥ t + 1 > 0, then there exists a t - (v, t + 1, (t + 1)!(2t+1)) design. We prove that if there exists a (t + 1) - (v, k, λ) design and a t - (v - 1, k - 2, λ(k - t - 1) / (v - k + 1)) design with t ≥ 2, then there exists a t - (v + 1, k, λ(v - t + 1)(v - t) / (v - k + 1)(k - t)) design. Using this recursive construction, we prove that for any pair (t, n) of integers (f ≥ 2 and n ≥ 0), there exists a simple non trivial t - (v, k, λ) design having an automorphism group isomorphic to ℤn2.SCOPUS: ar.j