Related pages

Symmetric designs
Steiner systems
A design is a finite incidence structure with and for each line , such that each subset of size t is contained in exactly lines. Lines are often called blocks in this context. Moreover, it's convenient to assume . A design with t=2 and is called a block plan.

Given a set with v elements and a number , we may choose all k element subsets of as our blocks. This structure is a design for all with

These designs are called the trivial designs. Each design is also a design for each with

In particular, the number of lines is exactly

Some types of designs have special names, for example


Contributed by Hauke Klein
Version $Id: design.html,v 1.1 2000/12/26 18:28:09 hauke Exp $