Uniform designs have been widely used in physical and computer experiments due to their robust performances. The level permutation method can efficiently construct uniform designs with both lower discrepancy and less aberration. However, the related existing literature has mostly discussed uniform fixed-level designs, the construction of uniform mixed-level designs has been quite few studied. In this paper, a novel level permutation method for constructing uniform mixed-level designs is proposed. Our main idea is to perform level permutations on a new class of designs, called minimum average discrepancy designs, rather than generalized minimum aberration designs as in the fixed-level case. Several theoretical results on the design optimality and construction are obtained. Numerical results suggest the good performance of the resulting designs under various popular discrepancies.

由于其稳健的性能，均匀设计已广泛用于物理和计算机实验。水平排列方法可以有效地构建具有较低差异和较少像差的统一设计。然而，现有的相关文献大多讨论了统一的固定水平设计，而关于统一混合水平设计的构建研究却很少。在本文中，提出了一种用于构建均匀混合级别设计的新级别排列方法。我们的主要想法是对一类新的设计执行级别排列，称为最小平均差异设计，而不是像固定级别情况下的广义最小像差设计。获得了关于设计优化和施工的几个理论结果。