Construction of Partial Diallel Cross Plan and its Operations

In this chapter, a new method of constructing a partial diallel cross plan using the cubic lattice partially balanced incomplete block designs of three associated classes with parameters v = s3 , b = 2 s3 , r = 4 , k = 2,λ 1 = 1, λ2 and λ3 = 1, where S≥2 is proposed. Diallel crosses are used to investigate the genetic features of inbred lines in plant breeding operations. Only the effects of the general combining ability were estimated in the linear model, and the crosses were chosen based on the association scheme. Each cross occurs a maximum of one time in the construction of a partial diallel cross plan, and as the number of lines (v) increases, the efficiency (Ep) decreases and efficiency factor ( E*) per cross increases. The Cubic Lattice PBIB design with three associate class were used to construct the partial diallel cross plans to estimate the GCA effects and the efficiency Ep decreases and the efficiency factor E* per cross increases, provided v is large.