A COMPLEMENTARY SET THEORY FOR QUATERNARY CODE DESIGNS

• 成果类型: Article
• 署名作者: Mukerjee, Rahul; Tang, Boxin
• 署名单位: Indian Institute of Management (IIM System); Indian Institute of Management Calcutta; Simon Fraser University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1160
• 发表日期: 2013
• 页码: 2768-2785
• 关键词: fractional factorial-designs; minimum aberration; nonregular designs; one-8th

摘要

Quaternary code (QC) designs form an attractive class of nonregular factorial fractions. We develop a complementary set theory for characterizing optimal QC designs that are highly fractionated in the sense of accommodating a large number of factors. This is in contrast to existing theoretical results which work only for a relatively small number of factors. While the use of imaginary numbers to represent the Gray map associated with QC designs facilitates the derivation, establishing a link with foldovers of regular fractions helps in presenting our results in a neat form.