On the construction of E- and MV-optimal group divisible designs with unequal block sizes

Abstract

In this note we consider experimental situations in which ν treatments are being tested in b blocks where b i blocks contain k i experimental units, i = 1, 3., p, k 1≤ k 2≤3.≤ k p . Some methods for constructing group divisible designs having unequal block sizes of the types proven E- and MV-optimal in Lee and Jacroux (1985) are given. The methods given are analogous to those used by Gupta and Jones (1983) to construct variance balanced designs with unequal block sizes from group divisible designs. A table of some E- and MV-optimal group divisible designs with two different block sizes and having treatmetns replicated fewer than twenty-five times is also given.