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Construction of four-level and mixed-level designs with zero Lee discrepancy

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Abstract

The uniformity criterion under Lee discrepancy favors designs with the smallest Lee discrepancy value. Based on quaternary codes, the present paper explores the construction of four-level and mixed two- and four-level fractional factorial designs with zero Lee discrepancy. A general construction method is provided, and our theoretic results show that designs with zero Lee discrepancy can be obtained from two-level full factorial designs. When measuring uniformity by Lee discrepancy, designs with a value of zero apparently are optimal. In particular, an additional lower bound on Lee discrepancy is not required.

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Acknowledgements

The authors thank the Editor in Chief, an associate editor and two reviewers for their helpful comments. This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 11561025, 11701213), Provincial Natural Science Foundation of Hunan (Grant Nos. 2017JJ2218, 2017JJ3253), Scientific Research Plan Item of Hunan Provincial Department of Education (Grant No. 18A284), Science and Innovation Plan Item of Xiangxi Autonomous Prefecture (Grant Nos. 2018SF5022, 2018SF5023).

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  1. College of Mathematics and Statistics, Jishou University, Jishou, 416000, China

    Liuping Hu, Zujun Ou & Hongyi Li

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  1. Liuping Hu
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  2. Zujun Ou
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  3. Hongyi Li
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Correspondence to Hongyi Li.

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Hu, L., Ou, Z. & Li, H. Construction of four-level and mixed-level designs with zero Lee discrepancy. Metrika 83, 129–139 (2020). https://doi.org/10.1007/s00184-019-00720-x

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  • DOI: https://doi.org/10.1007/s00184-019-00720-x

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