This paper investigates the construction of row–column designs for \({3}^{n}\) factorial experiments arranged in three rows, with the objective of estimating main effects and two-factor interactions under incomplete blocking. A single-replicate construction based on generating matrices is proposed, which ensures unconfounded estimation of all main effects with full efficiency. Due to inherent structural constraints, only a subset of two-factor interactions can be estimated within a single replicate. To improve interaction estimation, a multi-replicate construction is developed using a greedy set-cover approach that combines admissible principal blocks. The proposed procedure yield designs with near-minimal replications while enhancing the overall efficiency of two-factor interactions. Theoretical justification is provided through balance conditions and a confounding criterion for estimability. A R-package named “rcd3” has also been developed using the proposed algorithm as a facility to generate efficient row-column designs for 3-level factorial experiments in 3 rows. The performance of the proposed constructions is examined with respect to the upper bound on unconfounded two-factor interactions, and results for up to eight factors are presented.
