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May 9, 2026Theory of Probability and Its Applications0 citations

Uniformity of Mixed Two- and Four-Level Designs under Quaternary Codes

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XFXiangyu FangHLHongyi LiYLYiju Lei

Key Points

  • The central aim is to transform mixed two- and four-level designs into two-level designs and study their uniformity via wrap-around L2-discrepancy.
  • Applied two types of quaternary coding mapping to transform designs.
  • Studied uniformity characteristics measured by wrap-around L2-discrepancy.
  • Calculated lower bounds for wrap-around L2-discrepancy in mixed designs.
  • Obtained lower bounds for wrap-around L2-discrepancy for both design types.
  • Demonstrated tightness of bounds through three numerical examples.
  • These bounds serve as benchmarks for constructing uniform mixed designs.

Abstract

In this paper, mixed two- and four-level designs are transformed to two-level designs via two types of quaternary coding mapping, and the uniformity measured by wrap-around L₂-discrepancy of mixed two- and four-level designs is studied, respectively. Some lower bounds of wrap-around L₂-discrepancy for mixed two- and four-level designs are obtained, three numerical examples are provided to illustrate the theoretical results, and it is shown that these lower bounds are tight, which can serve as a benchmark in the construction of uniform mixed two- and four-level designs.

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Cite This Study

Fang et al. (2026) studied this question.

synapsesocial.com/papers/69fecfafb9154b0b82876a77https://doi.org/10.1137/s0040585x97t992781
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