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April 2011 A trigonometric approach to quaternary code designs with application to one-eighth and one-sixteenth fractions
Runchu Zhang, Frederick K. H. Phoa, Rahul Mukerjee, Hongquan Xu
Ann. Statist. 39(2): 931-955 (April 2011). DOI: 10.1214/10-AOS815

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.

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Runchu Zhang. Frederick K. H. Phoa. Rahul Mukerjee. Hongquan Xu. "A trigonometric approach to quaternary code designs with application to one-eighth and one-sixteenth fractions." Ann. Statist. 39 (2) 931 - 955, April 2011. https://doi.org/10.1214/10-AOS815

Information

Published: April 2011
First available in Project Euclid: 8 April 2011

zbMATH: 1215.62075
MathSciNet: MR2816343
Digital Object Identifier: 10.1214/10-AOS815

Subjects:
Primary: 62K15

Keywords: Aliasing index , branching technique , generalized minimum aberration , generalized resolution , Gray map , nonregular design , projectivity

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 2 • April 2011
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