  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.
