U-型设计的对称化L2-偏差的下界

数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1802-1811.

U-型设计的对称化L₂-偏差的下界

雷轶菊¹(),欧祖军^2,*()

¹ 新乡学院数学与统计学院, 河南新乡 453003
² 吉首大学数学与统计学院, 湖南吉首 416000

收稿日期:2021-07-22 出版日期:2022-12-26 发布日期:2022-12-16
通讯作者: 欧祖军 E-mail:leiyiju2001@sina.com;ozj9325@mail.ccnu.edu.cn
作者简介:雷轶菊, E-mail: leiyiju2001@sina.com
基金资助:
国家自然科学基金(11961027);国家自然科学基金(12161040);国家自然科学基金(11701213);湖南省自然科学基金(2021JJ30550);湖南省自然科学基金(2020JJ4497)

Lower Bounds for the Symmetric L₂-Discrepancy of U-type Designs

Yiju Lei¹(),Zujun Ou^2,*()

¹ College of Mathematics and Statistics, Xinxiang University, Henan xinxiang 453003
² College of Mathematics and Statistics, Jishou University, Hunan Jishou 416000

Received:2021-07-22 Online:2022-12-26 Published:2022-12-16
Contact: Zujun Ou E-mail:leiyiju2001@sina.com;ozj9325@mail.ccnu.edu.cn
Supported by:
the NSFC(11961027);the NSFC(12161040);the NSFC(11701213);the Natural Science Foundation of Hunan Province(2021JJ30550);the Natural Science Foundation of Hunan Province(2020JJ4497)

摘要/Abstract

摘要：

均匀设计是部分因子设计的主要方法之一, 已被广泛地应用于工业生产、系统工程、制药及其他自然科学中.各种偏差被用来度量部分因子设计的均匀性, 其关键的问题是寻找一个精确的偏差下界, 因为它可以作为衡量设计均匀性的标准.该文给出了4水平对称U-型设计的对称化L₂-偏差的下界, 以及2、3混水平和2、4混水平非对称U-型设计的对称化L₂-偏差的下界

关键词: U-型设计, 对称化L₂-偏差, 下界

Abstract:

Uniform design is one of the main methods of fractional factorials, which has been widely used in industrial production, systems engineering, pharmacy and other natural sciences. Various discrepancies are used to measure the uniformity of fractional factorials, the key is to find an accurate lower bound of the discrepancy, because it can be used as a benchmark which measures uniformity of design. In this paper, the lower bounds for the symmetric L₂-discrepancy on symmetrical U-type designs with four-level and asymmetrical U-type designs with two and three mixed levels and two and four mixed levels are abtained.

Key words: U-type design, Symmetric L₂-discrepancy, Lower bound

中图分类号:

O212.6

雷轶菊,欧祖军. U-型设计的对称化L₂-偏差的下界[J]. 数学物理学报, 2022, 42(6): 1802-1811.

Yiju Lei,Zujun Ou. Lower Bounds for the Symmetric L₂-Discrepancy of U-type Designs[J]. Acta mathematica scientia,Series A, 2022, 42(6): 1802-1811.

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U-型设计的对称化L₂-偏差的下界

Lower Bounds for the Symmetric L₂-Discrepancy of U-type Designs

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