Optimal Partial Diallel Cross Plan and Its Constructions

Abstract

In this chapter, a new method of constructing a partial diallel cross plan using the two blocked (equal block) and unblocked (unequal block) balanced incomplete block designs \(d_1\) and \(d_2\), and each design has two sets of parameters \(m_1, m_2\), and \(n_1, n_2\), where \(S_0 \geq 6\) with parameters \(v, b, r, k\) and \(\lambda\), is proposed. In plant breeding operations, diallel crossings are employed to explore the genetic characteristics of inbred lines. Using the linear model, estimated only the general combining ability effects. The crosses were taken based on the design parameters, and each cross occurred only once in constructing the partial diallel cross plan. When the number of lines \((v)\) increases, the efficiency factor \(\left(E_p\right)\) and efficiency factor \(\left(E^*\right)\) per cross will increase. The constructed method is also illustrated with a suitable example. The MS-optimality criterion is significantly more straightforward than traditional criteria since it allows for algebraic findings in an area where different criteria are typically only evaluated numerically, design by design.