Some E and MV-optimal designs for the two-way elimination of heterogeneity

Summary It is well known that in experimental settings wherev treatments are being tested inb blocks of sizek, a group divisible design having parametersλ ₂=λ₂+1 and whose correspondingC-matrix has maximal trace is both E and MV-optimal among all possible competing designs. In this paper, we show that under certain conditions, the E and MV-optimal group divisible block designs mentioned in the previous sentence can be used to construct E and MV-optimal row-column designs to handle experimental situations in which heterogeneity is to be eliminated in two directions and wherev treatments are being tested inb columns andk rows. Examples are given to illustrate how the results obtained can be applied. Research sponsored in part by National Science Foundation Grant No. DMS-8401943.