We consider designs for $f$ factors each at $m$ levels, where $f$ is small but $m$ is large. Main effect designs with $mf$ experimental points are presented. For two factors, two types of designs are investigated, termed sawtooth and dumbbell designs, based on a graphical representation. For three factors, cyclic sawtooth designs are considered. The paper seeks optimal and near optimal designs which involve factors with many levels but few observations. It also investigates issues of robustness when as much as one third of the data is structurally missing. An important area of application is in screening for drug discovery and we compare our designs with others using a published data set with two factors each with fifty levels, where the dumbbell design outperforms others and is an example of an inherently unbalanced design dominating more balanced designs.
Philip J. Brown. Martin S. Ridout. "Level-screening designs for factors with many levels." Ann. Appl. Stat. 10 (2) 864 - 883, June 2016. https://doi.org/10.1214/16-AOAS916