Optimal orthogonal designs for experiments with four-level and two-level factors

Experiments with both four-level and two-level factors have been conducted in many different domains, ranging from engineering to ergonomics. In such experiments, the four-level factors are used in three different ways: as blocking factors, as qualitative factors, or as quantitative factors. However, it was generally not easy for the authors to find an appropriate design for their experiment. A solution to this problem is to use a catalog of designs with a wide range of options. To efficiently use such a catalog, one needs criteria to identify the best designs. We present good criteria for the three different usages of four-level factors, and we apply these criteria to the catalog of Bohyn et al. (J R Stat Soc Ser C: Appl Stat 72:750–769, 2023). Finally, we present tables of four-and-two-level designs that are optimal with respect to the different criteria, for run sizes 16, 32, 64 and 128, with 1, 2, or 3 four-level factors, and up to 20 two-level factors.