LAUSR

Level permutations of factors can improve space-filling properties of designs, and the properties of the three-level Triple designs constructed by tripling method are related to original designs. In this paper, a new strategy for tripling is provided for constructing three-level uniform designs. By considering all possible level permutations of factors, the relationship is built between the average squared centered $$L_2$$ -discrepancy value of the Triple design and the wordlength pattern of the original design, which provides a theoretical basis for selecting a uniform design from an original design with minimum aberration by the level permutations. Moreover, the projection uniformity of the Triple design and its original design is considered, and the relationship of the uniformity pattern between the Triple design and its original design is built. Finally, some numerical results are used to support our theoretical results.