Quarter-fraction factorial designs constructed via quaternary codes

TL;DR

This paper investigates the use of quaternary codes to construct quarter-fraction nonregular factorial designs, achieving designs with superior resolution and projectivity compared to regular designs, and providing theoretical insights into their aliasing structures.

Contribution

It introduces a methodology for constructing high-quality nonregular designs using quaternary codes, with theoretical analysis and optimal design criteria.

Findings

Designs have larger generalized resolution than regular designs.

Some designs achieve generalized minimum aberration and maximum projectivity.

Theoretical results on aliasing structures of these designs.

Abstract

The research of developing a general methodology for the construction of good nonregular designs has been very active in the last decade. Recent research by Xu and Wong [Statist. Sinica 17 (2007) 1191--1213] suggested a new class of nonregular designs constructed from quaternary codes. This paper explores the properties and uses of quaternary codes toward the construction of quarter-fraction nonregular designs. Some theoretical results are obtained regarding the aliasing structure of such designs. Optimal designs are constructed under the maximum resolution, minimum aberration and maximum projectivity criteria. These designs often have larger generalized resolution and larger projectivity than regular designs of the same size. It is further shown that some of these designs have generalized minimum aberration and maximum projectivity among all possible designs.