, Volume 82, Issue 5, pp 573–587 | Cite as

Constructing optimal four-level designs via Gray map code

  • Liuping Hu
  • Hongyi Li
  • Zujun OuEmail author


Recent research indicates that optimal designs can be constructed based on coding theory. This paper explores the use of Gray map code to construct optimal four-level designs. A general construction of four-level designs is described and some theoretic results are obtained. Many four-level designs constructed by the method often possess nice properties, such as less aberration and lower discrepancy. Moreover, the method is useful to construct those of four-level designs with large size.


Gray map Aberration Uniformity Lee discrepancy 



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, 11871237), Provincial Natural Science Foundation of Hunan (Grant Nos. 2017JJ2218, 2017JJ3253) and Science and Innovation Plan Item of Xiangxi Autonomous Prefecture (Grant Nos. 2018SF5022, 2018SF5023).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mathematics and StatisticsJishou UniversityJishouChina

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