| CONSTRUCTING UNIFORM DESIGNS WITH TWO- OR THREE-LEVEL |
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| 作者姓名： | 覃红 张尚立 方开泰 |
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| 作者单位： | Department of Mathematics Central China Normal University Wuhan 430079，China Department of Mathematics，Hong Kong Baptist University，Hong Kong，China，Department of Mathematics Beijing Jiaotong University，Beijing 100044，China，Department of Mathematics Hong Kong Baptist University，Hong Kong，China |
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| 基金项目： | This work was partially supported by the NNSF of China(10441001) the Project sponsored by SRF for ROCS (SEM) the NSF of Hubei Province. The second author's research was also partially supported by the Pre-studies Project of NBRP (2003CCA2400) |
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| 摘 要： | 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.
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| 关 键 词： | 差异 Hadamard矩阵 加重平衡距离 统一设计 |
| 收稿时间： | 2004-03-07 |
| 修稿时间： | 2005-09-13 |
CONSTRUCTING UNIFORM DESIGNS WITH TWO- OR THREE-LEVEL |
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| Qin Hong, Zhang Shangh, Fang Kaitai.CONSTRUCTING UNIFORM DESIGNS WITH TWO- OR THREE-LEVEL[J].Acta Mathematica Scientia,2006,26(3):451-459. |
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| Authors: | Qin Hong Zhang Shangh Fang Kaitai |
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| 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. |
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| Keywords: | Discrepancy Hadamard matrix Hamming distance uniform design |
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