Constructing optimal four-level designs via Gray map code
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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.
KeywordsGray 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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