Abstract:

When the number of runs is large, to search for uniform designs in the sense of low-discrepancy is an NP hard problem. The number of runs of most of the available uniform designs is small (≤ 50). In this article, the authors employ a kind of the so-called Hamming distance method to construct uniform designs with two- or three-level such that some resulting uniform designs have a large number of runs. Several infinite classes for the existence of uniform designs with the same Hamming distances between any distinct rows are also obtained simultaneously. Two measures of uniformity, the centered L₂-discrepancy (CD, for short) and wrap-around L₂-discrepancy (WD, for short), are employed.

Key words: Discrepancy, Hadamard matrix, Hamming distance, uniform design