The concept of relative t-designs for Q-polynomial association schemes is due to Delsarte(Philips Res Rep 32: 373C411, 1997). In this paper, we discuss the Fisher type lower bounds of tight relative 6-designs very exp...The concept of relative t-designs for Q-polynomial association schemes is due to Delsarte(Philips Res Rep 32: 373C411, 1997). In this paper, we discuss the Fisher type lower bounds of tight relative 6-designs very explicitly for binary Hamming association schemes H(n, 2).展开更多
Association scheme is a structure on a finite set that has some special relations among elements in the set. These relations are usually hidden in other relations, so how to derive them out is a problem. The paper giv...Association scheme is a structure on a finite set that has some special relations among elements in the set. These relations are usually hidden in other relations, so how to derive them out is a problem. The paper gives a constructing method of mending parameters of the association schemes, and a new family of association schemes is obtained： quasiFmetric association scheme.展开更多
The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical ind...The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical industry, etc. In this paper, a new series of generalized partially balanced incomplete blocks PBIB designs with m associated classes (m = 4, 5 and 7) based on new generalized association schemes with number of treatments v arranged in w arrays of n rows and l columns (w ≥ 2, n ≥ 2, l ≥ 2) is defined. Some construction methods of these new PBIB are given and their parameters are specified using the Combinatory Method (s). For n or l even and s divisor of n or l, the obtained PBIB designs are resolvable PBIB designs. So the Fang RBIBD method is applied to obtain a series of particular U-type designs U (wnl;) (r is the repetition number of each treatment in our resolvable PBIB design).展开更多
基金Supported by the Natural Science Foundation of Hebei Province（A2013408009） Sup- ported by the Specialized Research Fund for the Doctoral Program of Higher Education（20121303110005）+1 种基金 Supported by the Natural Science Foundation of Hebei Education Department（ZH2012082） Supported by the Foundation of Langfang Teachers University（LSBS201205）
文摘The concept of relative t-designs for Q-polynomial association schemes is due to Delsarte(Philips Res Rep 32: 373C411, 1997). In this paper, we discuss the Fisher type lower bounds of tight relative 6-designs very explicitly for binary Hamming association schemes H(n, 2).
文摘Association scheme is a structure on a finite set that has some special relations among elements in the set. These relations are usually hidden in other relations, so how to derive them out is a problem. The paper gives a constructing method of mending parameters of the association schemes, and a new family of association schemes is obtained： quasiFmetric association scheme.
文摘The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical industry, etc. In this paper, a new series of generalized partially balanced incomplete blocks PBIB designs with m associated classes (m = 4, 5 and 7) based on new generalized association schemes with number of treatments v arranged in w arrays of n rows and l columns (w ≥ 2, n ≥ 2, l ≥ 2) is defined. Some construction methods of these new PBIB are given and their parameters are specified using the Combinatory Method (s). For n or l even and s divisor of n or l, the obtained PBIB designs are resolvable PBIB designs. So the Fang RBIBD method is applied to obtain a series of particular U-type designs U (wnl;) (r is the repetition number of each treatment in our resolvable PBIB design).
