Construction of 2fi-optimal row-column designs

Row-column designs that provide unconfounded estimation of all main effects and the maximum number of two-factor interactions (2fi's) are called 2fi-optimal. This issue has been paid great attention recently for its wide application in industrial or physical experiments. The constructions of 2fi-optimal two-level and three-level full factorial and fractional factorial row- column designs have been proposed. However, the results for higher prime levels have not been achieved yet. In this paper, we give theoretical constructions of 2fi-optimal s n full factorial row-column designs for any odd prime level s and any parameter combination, and theoretical constructions of 2fi-optimal s n - 1 fractional factorial row-column designs for any prime level s and any parameter combination.