Block designs

This paper is concerned with the theory of block designs, a part of modern combinatorics. Originally block designs arose in mathematical statistics (design of experiments, treatment of experimental variables); but nowadays they are investigated by many mathematicians for their own sake. The purpose of our paper is to give an account of the foundations of the theory of block designs and a survey of recent results. The paper contains three main sections: in the first section the algebraic and combinatorial properties of block designs are described, in particular, properties of BIB- and PBIB-designs; in the second section relationships between block designs and other combinatorial configurations are investigated; and the last section is devoted to the main existence theorems and to construction methods for block designs.