Abstract

Space-filling designs are widely used in various fields because of their nice space-filling properties. Uniform designs are one of space-filling designs, which desires the experimental points to scatter uniformly over the experimental area. For practical need, the construction and their properties of nine-level uniform designs are discussed via two code mappings in this paper.

Firstly, the algorithm of constructing nine-level uniform designs is presented from an initial three-level design by the Type-I code mapping and tripling technique. Secondly, the algorithm of constructing nine-level uniform designs is presented from a three-level base design by the Type-II code mapping and generalized orthogonal arrays. Moreover, relative properties are discussed based on the two code mappings. Finally, some numerical examples are given out for supporting our theoretical results.