A code arithmetic approach for quaternary code designs and its application to (1/64)th-fractions

TL;DR

This paper develops a theoretical framework for quaternary code-based fractional factorial designs, characterizing their properties and demonstrating their potential for more cost-effective experimental designs compared to traditional methods.

Contribution

It introduces a new theory for analyzing quaternary code designs, specifically for (1/4)^p and (1/64)th-fractions, improving understanding of their structure and efficiency.

Findings

Some QC designs outperform regular fractional designs in cost-efficiency.

The paper reveals a periodic structure related to resolution in (1/64)th-fraction QC designs.

Examples demonstrate the practical advantages of QC designs over traditional methods.

Abstract

The study of good nonregular fractional factorial designs has received significant attention over the last two decades. Recent research indicates that designs constructed from quaternary codes (QC) are very promising in this regard. The present paper aims at exploring the fundamental structure and developing a theory to characterize the wordlengths and aliasing indexes for a general $(1/4)^p$th-fraction QC design. Then the theory is applied to (1/64)th-fraction QC designs. Examples are given, indicating that there exist some QC designs that have better design properties, and are thus more cost-efficient, than the regular fractional factorial designs of the same size. In addition, a result about the periodic structure of (1/64)th-fraction QC designs regarding resolution is stated.