Designs for screening experiments usually include factors with two levels only. Adding a few four-level factors allows for the inclusion of multi-level categorical factors or quantitative factors with possible quadratic or third-order effects. Three examples motivated us to generate a large catalog of designs with two-level factors as well as four-level factors. To create the catalog, we considered three methods. In the first method, we select designs using a search table, and in the second method, we use a procedure that selects candidate designs based on the properties of their projections into fewer factors. The third method is actually a benchmark method, in which we use a general orthogonal array enumeration algorithm. We compare the efficiencies of the new methods for generating complete sets of non-isomorphic designs. Finally, we use the most efficient method to generate a catalog of designs with up to three four-level factors and up to 20 two-level factors for run sizes 16, 32, 64, and 128. In some cases, a complete enumeration was infeasible. For these cases, we used a bounded enumeration strategy instead. We demonstrate the usefulness of the catalog by revisiting the motivating examples.

翻译：筛选实验的设计通常仅包含二水平因子。引入少量四水平因子可纳入多水平分类因子或可能存在二次或三次效应的定量因子。三个实际案例促使我们构建一个包含二水平与四水平因子的大型设计目录。为实现该目录，我们考虑了三种方法：第一种方法通过搜索表选取设计，第二种方法基于设计向更少因子投影的性质选择候选设计，第三种方法实质上是基准方法，采用通用正交阵列枚举算法。我们比较了生成完备非同构设计集的新方法效率，最终使用最高效方法生成了运行规模为16、32、64和128时，最多含三个四水平因子及至多二十个二水平因子的设计目录。对于完全枚举不可行的情况，我们改用有界枚举策略。通过重新审视三个原始案例，验证了该设计目录的实用价值。