Partially balanced bipartite block designs

Abstract

This article provides some new construction methods of partially balanced bipartite block (PBBB) designs for comparing test treatments with more than one control. Partially balanced incomplete block (PBIB) designs based on some association schemes such as triangular association, Latin-square association, group divisible association, and cyclic association are used for developing these methods of construction. A catalog of efficient PBBB designs is included for parameter values v1 (number of test treatments) ≤10, v2 (number of control treatments) =2,b (number of blocks) ≤8,r1 (replications of test treatments) ≤10 and k (block size) ≤6 along with computed variances.