Archiv der Mathematik

, Volume 110, Issue 5, pp 459–466 | Cite as

Half of an antipodal spherical design

  • Eiichi Bannai
  • Da Zhao
  • Lin Zhu
  • Yan Zhu
  • Yinfeng Zhu
Article
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Abstract

We investigate several antipodal spherical designs on which we can choose half of the points, one from each antipodal pair, such that they are balanced at the origin. In particular, root systems of type A, D and E, minimal points of the Leech lattice, and the unique tight 7-design on \(S^{22}\) are studied. We also study a half of an antipodal spherical design from the viewpoint of association schemes and spherical designs of harmonic index T.

Keywords

Spherical design Leech lattice Antipodal 

Mathematics Subject Classification

05B30 05B35 
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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesShanghai Jiao Tong UniversityShanghaiChina

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