Some nonregular designs from the Nordstrom-Robinson code and their statistical properties

• 成果类型: Article
• 署名作者: Xu, HQ
• 署名单位: University of California System; University of California Los Angeles
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/92.2.385
• 发表日期: 2005
• 页码: 385397
• 关键词: fractional factorial-designs; minimum aberration criteria; split-plot designs; projection properties; orthogonal arrays; optimal blocking; plackett-burman; 2-level; RESOLUTION; search

摘要

The Nordstrom-Robinson code is a well-known nonlinear code in coding theory. This paper explores the statistical properties of this nonlinear code. Many nonregular designs with 32, 64, 128 and 256 runs and 7-16 factors are derived from it. It is shown that these nonregular designs are better than regular designs of the same size in terms of resolution, aberration and projectivity. Furthermore, many of these nonregular designs are shown to have generalised minimum aberration among all possible designs. Seven orthogonal arrays are shown to have unique word-length pattern and four of them are shown to be unique up to isomorphism.