Locally trivial t-designs and t-designs without repeated blocks (Q1823945)

The author constructed non-trivial t-designs without repeated blocks for all t in an earlier paper [Non-trivial t-designs without repeated blocks exist for all t, Discrete Math. 65, 301-311 (1987; Zbl 0625.05005)]. A simpler proof of the main result in the preceding paper is given here. Also, he surveys known results and presents new results on partitioning the set of all \((t+1)\)-subsets of a v-set into \(S(\lambda;t,t+1,v)\) for the smallest possible value of \(\lambda\).