  Row-column factorial 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 high prime
level have not been achieved yet. In this paper, we develop these constructions
by giving a theoretical construction of $s^n$ full factorial 2fi-optimal
row-column designs for any odd prime level $s$ and any parameter combination,
and theoretical constructions of $s^{n-1}$ fractional factorial 2fi-optimal
row-column designs for any prime level $s$ and any parameter combination.
