Constructing optimal four-level designs via Gray map code (Q2312028)

In this paper the authors present a method to construct four-level symmetric designs with good uniformity properties, namely with low values of Lee discrepancy. The construction is based on the Gray map code, i.e., a binary design is defined first, and then two columns of the binary design are used to define a column in the four-level design. The main result in the paper is Theorem 5.1. It states that if the underlying binary design has less generalized aberration, then the four-level design built up with the Gray map has good properties in terms of Lee discrepancy.