Experimental Designs Using Digital Nets with Small Numbers of Points

Summary Digital nets can improve upon traditional fractional factorial designs because for a budget of n=bm runs, they can allow b, …, bm−1, or bm levels per factor, while retaining the good balance properties of orthogonal arrays. However, the t-value typically used to characterize the quality of digital nets is not adequate for the purposes of experimental design. Rather, concepts from the experimental design literature, such as strength, resolution and aberration should be used. Moreover, the known number-theoretic constructions of digital nets are optimized for large m, whereas for laboratory experiments one typically has n=bm less than 100. This article describes some recent work on constructing digital nets with small numbers of points that are suitable for experimental designs. Coding theory provides some bounds on the quality of designs that may be expected. The generating matrices for the designs are found by computational search. The quality of the designs obtained is compared with the coding theory bounds.