A-optimality of block designs for control versus test comparisons in diallel crosses is investigated. A sufficient condition for designs to be A-optimal is derived. Type S0 designs are defined and A-optimal type S0 designs are characterized. A lower bound to the A-efficiency of type S0 designs...

Several patterned methods of construction of nested group divisible (NGD) designs, starting from self-complementary group divisible (GD) designs and Hadamard matrices or GD designs, are given with some series of NGD designs. As a by-product, a new regular GD design is found.

In a proper non-binary variance-balanced design with parameters [nu], b,r1,..., r[nu], k (< [nu]), [rho], a new stringent upper bound [rho] [less-than-or-equals, slant] {[nu](k-1)/[k([nu]-1)]} x (min ri) is derived, where [rho] is the unique non-zero eigenvalue of the C-matrix of the design

Some new variance-balanced designs with unequal block sizes and unequal replications are presented by use of group divisible and triangular partially balanced incomplete block designs. Tables of such variance-balanced designs with replications no larger than 30 are provided.

This forms a sequel to Chacko and Dey (1979) who characterized chemical balance weighing designs optimum for the estimation of total weight. In this note, such optimum designs are completely characterized by showing the general construction.

Agarwal and Kumar (1986b) constructed variance-balanced (VB) ternary designs of [nu] treatments with a considerable reduction in number of experimental units as compared to the other existing block designs when [nu] - 1 is a prime. In this note, we shall show the existence of VB binary designs...

A simple method of construction of a semi-regular (SR) group divisible design from another SR group divisible design is given. Using this method, 111 available SR designs from Clatworthy (1973) and John and Turner (1977) are systematically classified into 20 classes. This procedure may produce...