Optimal row-column designs

Summary Row-column designs have been widely used in experiments involving double confounding. Among them, one that provides unconfounded estimation of all main effects and as many two-factor interactions as possible is preferred, and is called optimal. Most current work focuses on the construction of two-level row-column designs, while the corresponding optimality theory has been largely ignored. Moreover, most constructed designs contain at least one replicate of a full factorial design, which is not flexible as the number of factors increases. In this study, a theoretical framework is built up to evaluate the optimality of row-column designs with prime level. A method for constructing optimal row-column designs with prime level is proposed. Subsequently, optimal full factorial three-level row-column designs are constructed for any parameter combination. Optimal fractional factorial two-level and three-level row-column designs are also constructed for cost saving.