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.