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

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  • Hongquan Xu

Abstract

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. Copyright 2005, Oxford University Press.

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  • Hongquan Xu, 2005. "Some nonregular designs from the Nordstrom–Robinson code and their statistical properties," Biometrika, Biometrika Trust, vol. 92(2), pages 385-397, June.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:2:p:385-397
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    File URL: http://hdl.handle.net/10.1093/biomet/92.2.385
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    Cited by:

    1. Yang, Guijun & Butler, Neil A., 2007. "Nonregular two-level designs of resolution IV or more containing clear two-factor interactions," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 566-575, March.
    2. Yong-Dao Zhou & Hongquan Xu, 2017. "Composite Designs Based on Orthogonal Arrays and Definitive Screening Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1675-1683, October.
    3. VÁZQUEZ-ALCOCER, Alan & GOOS, Peter & SCHOEN, Eric D., 2016. "Two-level designs constructed by concatenating orthogonal arrays of strenght three," Working Papers 2016011, University of Antwerp, Faculty of Business and Economics.

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