Combinatorial design

Summary

A combinatorial design is a finite set together with a family of subsets, called blocks, that satisfies a balance condition. A typical condition is that every pair of points lies in the same number of blocks. Design theory studies when such systems exist and how to build them. The main families include block designs, Steiner systems, finite projective planes and, in a wider sense, Latin squares. Designs are used in the planning of experiments, in coding theory and in finite geometry.