## The Annals of Statistics

- Ann. Statist.
- Volume 40, Number 6 (2012), 3161-3175.

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

#### 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.

#### Article information

**Source**

Ann. Statist., Volume 40, Number 6 (2012), 3161-3175.

**Dates**

First available in Project Euclid: 22 February 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1361542078

**Digital Object Identifier**

doi:10.1214/12-AOS1069

**Mathematical Reviews number (MathSciNet)**

MR3097973

**Zentralblatt MATH identifier**

1296.62154

**Subjects**

Primary: 62K15: Factorial designs

**Keywords**

Quaternary-code design generalized minimum aberration generalized resolution generalized wordlength pattern aliasing index structure periodicity

#### Citation

Phoa, Frederick K. H. A code arithmetic approach for quaternary code designs and its application to (1/64)th-fractions. Ann. Statist. 40 (2012), no. 6, 3161--3175. doi:10.1214/12-AOS1069. https://projecteuclid.org/euclid.aos/1361542078