Construction of optimal supersaturated designs by the expansive replacement method

Abstract

Supersaturated design (SSD) plays an important role in screening factors. $E\left(f_{NOD}\right)$ criterion is one of the most widely used criteria to evaluate multi-level and mixed-level SSDs. This paper provides some methods to construct multi-level $E\left(f_{NOD}\right)$ optimal SSDs with general run sizes, which can also be extended to construct mixed-level SSDs. The main idea of these methods is combining two processed generalized Hadamard matrices with the expansive replacement method. These proposed methods are easy to perform. Besides, the non-orthogonality between any two columns of the resulting SSDs is well controlled by that of the source designs. Some illustrative examples are given and several new SSDs are provided in this paper.