Partial diallel crosses based on some association schemes with three and four associate classes

Abstract

The construction and analysis of partial diallel crosses based on some association schemes with three and four associate classes have been discussed. Characteristic roots and idempotent matrices have been used to simplify the analysis and to work out the average variance of the difference between the general combining ability effects of two parents or lines. It has been found that plans for partial diallel crosses based on Group Divisible Designs with three associate classes are clearly more efficient than those based on Simple Rectangular Lattice and Generalised Right Angular Designs both with four associate classes.