| Abstract: | A simple, straightforward procedure, which requires no special tables or generators, is presented for constructing resolvable incomplete block designs for v=pk, v=p2k, …, treatments, for k≥p, in incomplete blocks of size k. Also, it is shown, how to obtain incomplete block designs for any v in blocks of size k and k+1. The procedure allows construction of balanced incomplete block designs for p = k a prime number. For p = n not a prime number, incomplete block designs can be obtained by the procedure, but are not balanced. However, for ps being the smallest prime factor of n, ps + 1 for v = n2, ps2+ ps + 1 for v = n3, …, arrangements can be obtained for which the occurrence of any treatment pair in the blocks is either zero or one. This is called a zero-one concurrence design. Procedures are described for obtaining additional zero-one concurrence arrangements. It is shown that the efficiency of these designs is maximum. Both intra-block and inter-block analyses are described. |
