On the E(s^2)-optimality of two-level supersaturated designs constructed using Wu's method of partially aliased interactions on certain two-level orthogonal arrays

TL;DR

This paper extends Wu's method for constructing E(s^2)-optimal two-level supersaturated designs, proving optimality when starting from various orthogonal arrays with specific aliasing conditions.

Contribution

It generalizes previous results by establishing E(s^2)-optimality for designs based on any orthogonal array with up to three columns, under partial aliasing conditions.

Findings

Proves E(s^2)-optimality for designs from orthogonal arrays with n-1, n-2, or n-3 columns.

Extends Wu's method to a broader class of orthogonal arrays.

Provides theoretical validation for design optimality under specific aliasing structures.

Abstract

Wu [10] proposed a method for constructing two-level supersaturated designs by using a Hadamard design with n runs and n-1 columns as a staring design and by supplementing it with two-column interactions, as long as they are partially aliased. Bulutoglu and Cheng [2] proved that this method results in E(s^2)-optimal supersaturated designs when certain interaction columns are selected. In this paper, we extend these results and prove E(s^2)-optimality for supersaturated designs that are constructed using Wu's method when the starting design is any orthogonal array with n runs and n-1, n-2 or n-3 columns, as long as its main effects and two-column interactions are partially aliased with two-column interactions.