Combinatorial Design Theory

Variations on this definition are commonly considered, and the term ‘design’ includes these similar contexts. Design theory is a field of combinatorics with close ties to several other areas of mathematics including group theory, the theory of finite fields, the theory of finite geometries, number theory, combinatorial matrix theory, and graph theory, and with a wide range of applications in areas such as information theory, statistics, computer science, biology, and engineering. Like most areas of combinatorics, design theory has grown up with computer science and it has experienced a tremendous amount of growth in the last 30 years. The field has developed subfields and groups depending on the main techniques used: combinatorial, algebraic, and algorithmic/computational. There are also groups primarily involved with applications such as in coding theory, cryptography, and computer science. As design theory has grown, researchers have become increasingly specialized and focussed in subfields. In recent years, design