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两水平因子。引入少量四水平因子，可以纳入多水平分类因子或可能具有二次或三次效应的定量因子。三个实际案例促使我们生成一个包含两水平因子和四水平因子的设计大型目录。为创建该目录，我们考虑了三种方法。第一种方法通过搜索表选择设计；第二种方法基于设计在较少因子上的投影特性，采用选择候选设计的流程；第三种方法作为基准方法，使用通用的正交数组枚举算法。我们比较了新方法在生成完整非同构设计集时的效率。最终，采用最高效的方法，为运行次数为16、32、64和128的情况生成了包含至多三个四水平因子和至多二十个两水平因子的设计目录。在某些情况下，完全枚举不可行，此时我们采用有界枚举策略。通过重新审视案例问题，我们验证了该目录的实用性。