最小低阶混杂混合水平(2r)2n因子设计的一些结果

数学季刊 ›› 2007, Vol. 22 ›› Issue (1): 79-86.

最小低阶混杂混合水平(2^r)2ⁿ因子设计的一些结果

1.Department of Trade and Economics,Zhengzhou Electric Power College,Zhengzhou 450004,China; 2.Department of Basic Course,Henan Vocational College of Economy and Trade,Zhengzhou 450053,China; 3.Henan Province Computer Center,Zhengzhou 450008,China

收稿日期:2003-05-12 出版日期:2007-03-30 发布日期:2023-11-14
作者简介:SHI Cheng-tang(1955-),male,native of Changshu,Jiangsu,an associate professor of Zhengzhou Electric Power College,engages in applied mathematics.

Some Results on Minimum Aberration Mixed-level (2^r)2ⁿ Factorial Designs

1.Department of Trade and Economics,Zhengzhou Electric Power College,Zhengzhou 450004,China; 2.Department of Basic Course,Henan Vocational College of Economy and Trade,Zhengzhou 450053,China; 3.Henan Province Computer Center,Zhengzhou 450008,China

Received:2003-05-12 Online:2007-03-30 Published:2023-11-14
About author:SHI Cheng-tang(1955-),male,native of Changshu,Jiangsu,an associate professor of Zhengzhou Electric Power College,engages in applied mathematics.

摘要/Abstract

摘要： Mukerjee and Wu(2001) employed projective geometry theory to find the wordlength pattern of a regular mixed factorial design in terms of its complementary set, but only for the numbers of words of length 3 or 4.In this paper,by introducing a concept of consulting design and based on the connection between factorial design theory and cod- ing theory,we obtain some combinatorial identities that relate the wordlength pattern of a regular mixed-level (2^r)2ⁿ factorial design to that of its consulting design.Consequently,a general rule for identifying minimum aberration (2^r)2ⁿ factorial designs through their con- sulting designs is established.It is an improvement and generalization of the related result in Mukerjee and Wu(2001).

关键词: coding theory;consulting design;minimum aberration;mixed-level;regular, wordlength pattern

Abstract: Mukerjee and Wu(2001) employed projective geometry theory to find the wordlength pattern of a regular mixed factorial design in terms of its complementary set, but only for the numbers of words of length 3 or 4.In this paper,by introducing a concept of consulting design and based on the connection between factorial design theory and cod- ing theory,we obtain some combinatorial identities that relate the wordlength pattern of a regular mixed-level (2^r)2ⁿ factorial design to that of its consulting design.Consequently,a general rule for identifying minimum aberration (2^r)2ⁿ factorial designs through their con- sulting designs is established.It is an improvement and generalization of the related result in Mukerjee and Wu(2001).

Key words: coding theory;consulting design;minimum aberration;mixed-level;regular, wordlength pattern

中图分类号:

O157.4

史成堂, 张丹, 陈宝亭, 李玉凯. 最小低阶混杂混合水平(2^r)2ⁿ因子设计的一些结果[J]. 数学季刊, 2007, 22(1): 79-86.

SHI Cheng-tang, ZHANG Dan, CHEN Bao-ting, LI Yu-kai. Some Results on Minimum Aberration Mixed-level (2^r)2ⁿ Factorial Designs[J]. Chinese Quarterly Journal of Mathematics, 2007, 22(1): 79-86.

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最小低阶混杂混合水平(2^r)2ⁿ因子设计的一些结果

Some Results on Minimum Aberration Mixed-level (2^r)2ⁿ Factorial Designs

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