A trigonometric approach to quaternary code designs with application to one-eighth and one-sixteenth fractions

TL;DR

This paper introduces a trigonometric method to analyze quaternary code designs, leading to new theoretical insights and the identification of optimal fractional factorial designs with superior resolution and projectivity.

Contribution

It provides a systematic trigonometric framework for understanding quaternary code designs and discovers designs with maximum projectivity for one-eighth and one-sixteenth fractions.

Findings

Optimal QC designs often have higher generalized resolution.

Some designs achieve maximum projectivity among all designs.

The approach uncovers new theoretical results in fractional factorial design.

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 shows how a trigonometric approach can facilitate a systematic understanding of such QC designs and lead to new theoretical results covering hitherto unexplored situations. We focus attention on one-eighth and one-sixteenth fractions of two-level factorials and show that optimal QC designs often have larger generalized resolution and projectivity than comparable regular designs. Moreover, some of these designs are found to have maximum projectivity among all designs.