# nLab Steiner system

Steiner systems are combinatorial objects with main applications in finite geometries and finite group theory.

Given positive integers $l,n,m$ a Steiner system of type $S(l,n,m)$ is a pair of a set $S$ of cardinality $n$ and a set of subsets of $S$ of cardinality $m$, called blocks, such that every $l$-element subset of $S$ is in precisely one block.

Nontrivial Steiner systems occur for $1\lt l\lt n\lt m$.

Special cases are $S(2,3,n)$-s called Steiner triple systems and $S(3,4,n)$-s called Steiner quadruple systems.

Last revised on August 30, 2011 at 16:31:48. See the history of this page for a list of all contributions to it.