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<p>Uniform designs have excellent space-filling properties in whole experimental domain, but in practice, the projection uniformity of designs need be considered in low-dimensional space. In this paper, the average uniformity pattern of asymmetric designs is defined by the reproducing kernel function, and the minimum projection uniformity criterion is provided to screen the designs with better projection uniformity. Moreover, the analytical relationships between the average uniformity pattern and the generalized wordlength pattern, the orthogonal vector, the design efficiency respectively are built, an improved lower bound of the average uniformity pattern is obtained, which is used as a benchmark to measure the projection uniformity of asymmetric designs in different dimensions. Some numerical examples are provided to explain the theoretical results.</p>

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Projection uniformity of asymmetric designs based on average discrepancies

  • 期刊论文

  • 发表日期：

    2026年2月6日

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  • Jiezhong Tian,
  • Hongyi Li,
  • Shixian Zhang,
  • Yujia Xiao

摘要

Uniform designs have excellent space-filling properties in whole experimental domain, but in practice, the projection uniformity of designs need be considered in low-dimensional space. In this paper, the average uniformity pattern of asymmetric designs is defined by the reproducing kernel function, and the minimum projection uniformity criterion is provided to screen the designs with better projection uniformity. Moreover, the analytical relationships between the average uniformity pattern and the generalized wordlength pattern, the orthogonal vector, the design efficiency respectively are built, an improved lower bound of the average uniformity pattern is obtained, which is used as a benchmark to measure the projection uniformity of asymmetric designs in different dimensions. Some numerical examples are provided to explain the theoretical results.