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New results on quaternary codes and their Gray map images for constructing uniform designs

Author

Listed:
  • A. M. Elsawah

    (Zagazig University
    BNU-HKBU United International College)

  • Kai-Tai Fang

    (BNU-HKBU United International College
    The Chinese Academy of Sciences)

Abstract

The research of developing efficient methodologies for constructing optimal experimental designs has been very active in the last decade. Uniform design is one of the most popular approaches, carried out by filling up experimental points in a determinately uniform fashion. Applications of coding theory in experimental design are interesting and promising. Quaternary codes and their binary Gray map images attracted much attention from those researching design of experiments in recent years. The present paper aims at exploring new results for constructing uniform designs based on quaternary codes and their binary Gray map images. This paper studies the optimality of quaternary designs and their two and three binary Gray map image designs in terms of the uniformity criteria measured by: the Lee, wrap-around, symmetric, centered and mixture discrepancies. Strong relationships between quaternary designs and their two and three binary Gray map image designs are obtained, which can be used for efficiently constructing two-level designs from four-level designs and vice versa. The significance of this work is evaluated by comparing our results to the existing literature.

Suggested Citation

  • A. M. Elsawah & Kai-Tai Fang, 2018. "New results on quaternary codes and their Gray map images for constructing uniform designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(3), pages 307-336, April.
    • Handle: RePEc:spr:metrik:v:81:y:2018:i:3:d:10.1007_s00184-018-0644-5
    DOI: 10.1007/s00184-018-0644-5
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    References listed on IDEAS

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    1. A. M. Elsawah & Hong Qin, 2017. "Optimum mechanism for breaking the confounding effects of mixed-level designs," Computational Statistics, Springer, vol. 32(2), pages 781-802, June.
    2. A. M. Elsawah & Hong Qin, 2016. "Asymmetric uniform designs based on mixture discrepancy," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2280-2294, September.
    3. Zhou, Yong-Dao & Ning, Jian-Hui & Song, Xie-Bing, 2008. "Lee discrepancy and its applications in experimental designs," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1933-1942, September.
    4. Hong Qin & Mingyao Ai, 2007. "A note on the connection between uniformity and generalized minimum aberration," Statistical Papers, Springer, vol. 48(3), pages 491-502, September.
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    Cited by:

    1. A. M. Elsawah & Kai-Tai Fang & Ping He & Hong Qin, 2021. "Sharp lower bounds of various uniformity criteria for constructing uniform designs," Statistical Papers, Springer, vol. 62(3), pages 1461-1482, June.
    2. A. M. Elsawah, 2021. "Multiple doubling: a simple effective construction technique for optimal two-level experimental designs," Statistical Papers, Springer, vol. 62(6), pages 2923-2967, December.

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