Some new results on the uniform design (Q1895507)

The uniform design designs the experimental points to be uniformly scattered in the experimental domain. It has the advantages of good representation and fewer experiments, especially in the case of the number of levels being large. Since the uniform design was created, there have been a lot of successful applications in various fields: pharmaceutics, space techniques, chemical engineering, etc. Although the discrepancy is the universally-accepted measure of uniformity, it was difficult to compute it exactly in the past. Therefore, \textit{Y. Wang} and the first author [Kexue Tongbao, Foreign Lang. Ed. 26, 485-489 (1981; Zbl 0493.62068)] proposed a criterion based on approximation of the discrepancy. There are big errors sometimes, in particular when \(n\) is small we cannot find the uniform design with the smallest discrepancy. Here, in particular, we obtain many new uniform design tables with low discrepancy, which can significantly reduce the discrepancy of the uniform design given in the paper cited above.