Tripling of fractional factorial designs

Doubling and level permutation of factors are widely used in the construction of uniform designs and minimum aberration designs. Based on the viewpoint that double design is the orthogonal combination of all possible level permutations of its initial two-level design, a method of tripling for three-level design, which triples both the run size and number of factors of initial design, is proposed by orthogonally combining all possible level permutations of its initial design in this paper. The wrap-around L2-discrepancy of triple design is expressed by the wordlength pattern of its initial design, and a tight lower bound of the wrap-around L2-discrepancy of triple design is obtained. An efficient method for constructing uniform minimum aberration designs is proposed based on the projection of triple design. These constructed designs have better properties, such as minimum aberration and lower discrepancy, than existing uniform designs, and are recommended for use in practice.