Steiner system

Summary

A Steiner system $S(t, k, n)$ is a set of $n$ points with a family of $k$-element blocks. Every $t$ points lie in exactly one block. It is a block design with $\lambda = 1$. Steiner triple systems, finite projective planes and the large Witt design $S(5, 8, 24)$ are the best-known examples. The node Steiner system gives the precise definition.