CONSTRUCTING UNIFORM DESIGNS WITH TWO- OR THREE-LEVEL

• 出 处: 数学物理学报（英文版）
• 发表日期: 2004年期
• 关键词: Discrepancy Hadamard matrix Hamming distance uniform design
• 基金项目: the NNSF of China;the Project sponsored by SRF for ROCS (SEM) and the NSF of Hubei Province;The second author’s research was also partially supported by the Pre-studies Project of NBRP

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.