In many practical applications, follow-up experimental designs are commonly used to explore the relationship between inputs and outputs steps by steps. As some additional resources could be available to the experimenter after the first step, some additional runs or factors may be added in the follow-up stage. The issue of uniform augmented q-level designs is investigated in this paper. Using the level permutation technique, the uniformity of augmented q-level designs is discussed under the average mixture discrepancy, and new lower bounds of average mixture discrepancy for augmented designs are obtained, which can be served as the benchmark for searching uniform augmented designs. Numerical examples show that the uniform augmented designs can be constructed with high efficiency.

中文翻译：

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统一增强 q 级设计

在许多实际应用中，通常使用后续实验设计来逐步探索输入和输出之间的关系。由于在第一步之后实验者可以获得一些额外的资源，因此可能会在后续阶段添加一些额外的运行或因素。本文研究了统一增广 q 级设计的问题。使用级别置换技术，在平均混合差异下讨论了增广 q 级设计的均匀性，并获得了增广设计的平均混合差异的新下界，可作为搜索统一增广设计的基准。数值例子表明，可以高效地构建统一的增强设计。