(Received May 19, 1989; revised January 30, 1990)
Abstract. 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 b1 rows and b2 columns where row i has size k1i, i = 1,...., b1 and column j has size k2j, j = 1,...., b2. Conditions analogous to those given in Kunert (1983, Ann. Statist., 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.
Key words and phrases: Row-column design, block design, incidence matrix, balanced unequal block design.