ABSTRACT
Some methods for constructing balanced incomplete block designs were given in Section 1.2.1. Many of these designs can also be obtained very simply by a method of cyclic substitution. For example, a balanced incomplete block design for seven treatments in blocks of three is given by the seven blocks
Each treatment is replicated three times and every pair of treatments occurs together in a single block. The cyclic method of construction is such that a block is obtained by adding one to each element in the previous block and reducing modulo 7 when necessary. The full design can, therefore, be generated from one of the blocks, which is called the initial block. For convenience, the initial block will be taken to be the block of lowest numerical value. Hence, the above design is constructed by a cyclic development of the initial block (0 13).
