The methods of doubling and tripling have been used to construct two-level and three-level symmetrical fractional factorial designs with optimal properties. In this paper, the construction of symmetrical designs is generalized to an asymmetrical case, a novel construction method by amplifying is presented for constructing mixed two- and three-level uniform designs with large run sizes. The analytic relationship between the squared wrap-around \(L_2\)- discrepancy value of the amplified design constructed by amplifying and the wordlength pattern of the initial design is built. Furthermore, the relationships of uniformity and aberration between the amplified design and the corresponding initial design are respectively considered. These results provide a theoretical basis for constructing mixed two- and three-level uniform designs with large run sizes. Finally, some numerical results are provided to support our theoretical results.

已经使用加倍和三倍的方法来构造具有最佳特性的两级和三级对称分数阶乘设计。本文将对称设计的构造推广到一个不对称的情况，提出了一种通过放大的新颖构造方法来构造具有较大运行规模的混合二级和三级均匀设计。平方环绕\（L_2 \）之间的解析关系-通过放大构造的放大设计的差异值，并建立初始设计的字长样式。此外，分别考虑放大设计和相应的初始设计之间的均匀性和像差的关系。这些结果为构建具有较大运行量的混合二级和三级均匀设计提供了理论基础。最后，提供了一些数值结果来支持我们的理论结果。