Constructing optimal four-level designs via Gray map code

Recent research indicates that optimal designs can be constructed based on coding theory. This paper explores the use of Gray map code to construct optimal four-level designs. A general construction of four-level designs is described and some theoretic results are obtained. Many four-level designs constructed by the method often possess nice properties, such as less aberration and lower discrepancy. Moreover, the method is useful to construct those of four-level designs with large size.