Page "Combinatorics" Paragraph 17

Design theory is a study of combinatorial designs, which are collections of subsets with certain intersection properties.

Block designs are combinatorial designs of a special type.

This area is one of the oldest parts of combinatorics, such as in Kirkman's schoolgirl problem proposed in 1850.

The solution of the problem is a special case of a Steiner system, which systems play an important role in the classification of finite simple groups.

The area has further connections to coding theory and geometric combinatorics.