Construction and projection uniformity of three-level optimal supersaturated designs

Supersaturated designs are widely used for screening significant factors at the beginning of an experiment because of their economy and flexibility of runs. When a few factors are significant, the low-dimensional projection uniformity of designs is particularly important. In this article, a novel construction method called column augmentation is provided for constructing three-level optimal supersaturated designs. The method only starts from the initial three-level design with small columns and augments the columns by certain replacement rules instead of computer searching. The properties of the constructed designs are discussed, and some theoretical results show that when the initial design is A2-optimal, E(fNOD)-optimal, or equidistant under Hamming distance, the constructed three-level supersaturated design is E(fNOD)-optimal and the two-dimensional uniform projection design. Finally, some numerical examples are used to support the theoretical results.