Construction of 2fi-optimal row-column designs

TL;DR

This paper develops theoretical methods for constructing 2fi-optimal row-column factorial designs at any odd prime level, enabling unconfounded estimation of all main effects and maximum two-factor interactions.

Contribution

It provides the first theoretical constructions for 2fi-optimal designs at any odd prime level for both full and fractional factorials.

Findings

Constructed $s^n$ 2fi-optimal full factorial designs for any odd prime $s$.

Developed $s^{n-1}$ 2fi-optimal fractional factorial designs for any prime $s$.

Extended design construction to high prime levels where previous results were lacking.

Abstract

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.