Bounds on antipodal spherical designs with few angles

doi:10.37236/9891

CSpace

	Bounds on antipodal spherical designs with few angles
	Xu, Zhiqiang 1,2; Xu, Zili 1,2; Yu, Wei-Hsuan 3
	2021-08-13
发表期刊	ELECTRONIC JOURNAL OF COMBINATORICS
ISSN	1077-8926
卷号	28 期号:3 页码:21
摘要	A finite subset X on the unit sphere S-d is called an s-distance set with strength t if its angle set A(X) := {< x, y > : x, y is an element of X, x not equal y} has size s, and X is a spherical t-design but not a spherical (t + 1)-design. In this paper, we consider to estimate the maximum size of such antipodal set X for small s. Motivated by the method developed by Nozaki and Suda, for each even integer s is an element of [ t+5/2, t + 1] with t >= 3, we improve the best known upper bound of Delsarte, Goethals and Seidel. We next focus on two special cases: s = 3, t = 3 and s = 4, t = 5. Estimating the size of X for these two cases is equivalent to estimating the size of real equiangular tight frames (ETFs) and Levenstein-equality packings, respectively. We improve the previous estimate on the size of real ETFs and Levenstein-equality packings. This in turn gives an upper bound on vertical bar X vertical bar when s = 3, t = 3 and s = 4, t = 5, respectively.
DOI	10.37236/9891
收录类别	SCI
语种	英语
资助项目	Beijing Natural Science Foundation[Z180002] ; NSFC[12025108] ; NSFC[11688101]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000685640000001
出版者	ELECTRONIC JOURNAL OF COMBINATORICS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59114
专题	中国科学院数学与系统科学研究院
通讯作者	Xu, Zhiqiang
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math, LSEC, Beijing 100091, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Natl Cent Univ, Math Dept, Taoyuan, Taiwan
推荐引用方式 GB/T 7714	Xu, Zhiqiang,Xu, Zili,Yu, Wei-Hsuan. Bounds on antipodal spherical designs with few angles[J]. ELECTRONIC JOURNAL OF COMBINATORICS,2021,28(3):21.
APA	Xu, Zhiqiang,Xu, Zili,&Yu, Wei-Hsuan.(2021).Bounds on antipodal spherical designs with few angles.ELECTRONIC JOURNAL OF COMBINATORICS,28(3),21.
MLA	Xu, Zhiqiang,et al."Bounds on antipodal spherical designs with few angles".ELECTRONIC JOURNAL OF COMBINATORICS 28.3(2021):21.