E-optimality of some row and column designs

In this paper we consider experimental settings where treatments are being tested in b ₁ rows and b ₂ columns of sizes k _1i and k _2j , respectively, i=1,2,..., b ₁, j=1,2,..., b ₂. Some sufficient conditions for designs to be E-optimal in these classes are derived and some necessary and sufficient conditions for the E-optimality of some special classes of row and column designs are presented. Examples are also given to illustrate this theory.