A TRIGONOMETRIC APPROACH TO QUATERNARY CODE DESIGNS WITH APPLICATION TO ONE-EIGHTH AND ONE-SIXTEENTH FRACTIONS

• 成果类型: Article
• 署名作者: Zhang, Runchu; Phoa, Frederick K. H.; Mukerjee, Rahul; Xu, Hongquan
• 署名单位: Nankai University; Nankai University; Indian Institute of Management (IIM System); Indian Institute of Management Calcutta; University of California System; University of California Los Angeles; Academia Sinica - Taiwan; Northeast Normal University - China
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS815
• 发表日期: 2011
• 页码: 931-955
• 关键词: minimum aberration; factorial-designs; nonregular designs; projection

摘要

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.