On the determination and construction of optimal row-column designs having unequal row and column sizes

In this paper we consider experimental situations requiring usage of a row-column design where v treatments are to be applied to experimental units arranged in b ₁ rows and b ₂ columns where row i has size k _1i , i=1,..., b ₁ and column j has size k _2j , j=1,..., b ₂. Conditions analogous to those given in Kunert (1983, Ann. Statis., 11, 247–257) and Cheng (1978, Ann. Statist., 6, 1262–1272) are given which can often be used to establish the optimality of a given row-column design from the optimality of an associated block design. In addition, sufficient conditions are derived which guarantee the existence of an optimal row-column design which can be constructed by appropriately arranging treatments within blocks of an optimal block design.Visiting from the Indian Statistical Institute.