The Annals of Statistics

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

Runchu Zhang, Frederick K. H. Phoa, Rahul Mukerjee, and Hongquan Xu

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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.

Article information

Ann. Statist., Volume 39, Number 2 (2011), 931-955.

First available in Project Euclid: 8 April 2011

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Zentralblatt MATH identifier

Primary: 62K15: Factorial designs

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


Zhang, Runchu; Phoa, Frederick K. H.; Mukerjee, Rahul; Xu, Hongquan. A trigonometric approach to quaternary code designs with application to one-eighth and one-sixteenth fractions. Ann. Statist. 39 (2011), no. 2, 931--955. doi:10.1214/10-AOS815.

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