Sliced uniform designs are useful for generating experimental data with batch structures. In this paper, we employ the discrete discrepancy as the measure of uniformity to construct sliced uniform designs. The construction method is based on an important class of combinatorial configurations, namely, resolvable balanced incomplete block designs; hence, the construction method does not require any computer search. Through resolvable balanced incomplete block designs, under the discrete discrepancy, several infinite classes of new sliced uniform designs are obtained. The obtained design is optimal in the sense that not only the design as a whole but also each of its slices attain the lower bound of the discrete discrepancy. The design parameters are explicitly given, from which experimenters may choose an optimal sliced uniform design with the most suitable run size for their experiment.

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离散差异下最优切片均匀设计的构建方法

切片均匀设计对于生成具有批处理结构的实验数据很有用。在本文中，我们采用离散差异作为均匀性的度量来构建切片均匀设计。该构造方法基于一类重要的组合配置，即可解析的平衡不完全块设计；因此，该构造方法不需要任何计算机搜索。通过可解析的平衡不完全块设计，在离散差异下，得到了几个无限类的新切片均匀设计。获得的设计是最优的，因为不仅设计作为一个整体，而且它的每个切片都达到了离散差异的下限。明确给出了设计参数，