On the Theory of (M,S) Optimality in Incomplete Block Designs

The problem considered is the determination of optimal incomplete block designs when the experimental material does not fit any of the usual textbook situations. The criterion used to determine an optimal design within a given class Zr of incomplete block designs is the (M, S) optimality criterion Let C denote the matrix of coefficients obtained in the reduced normal equations for estimating the treatment effects in a given incomplete block design. The (M, S) optimality criterion is to find within the class.13d- the set of designs whose C-matrices have maximal trace, denoted by and then to find within those designs with mini-mum trace of C2; such a design is said to be (M, S) optimal. The classes of designs we consider are denoted b