On the construction of m-associate PBIB designs I

Abstract

The m-associate triangular association scheme has been discussed, and several series of partially balanced incomplete block ( PBIB) designs with m-associate triangular association scheme have been obtained in Section 1. In Section 2, an m-associate triangular-group divisible association scheme (T q — GD m , 1<q<m) has been introduced and several series of PBIB designs with m-associate triangular group divisible association scheme, from m-associate triangular PBIB designs have been constructed. Some numerical values to the three associate triangular designs, and three associate triangular group divisible designs in the range b, v≦100; r, k≦10, with their average efficiencies are given, respectively, in Tables I and II, in Section 3, where as usual v denotes the number of treatments, b the number of blocks, r the number of replications of each treatment, and k the block size.