Half of an antipodal spherical design

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.

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Correspondence to Da Zhao.

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Bannai, E., Zhao, D., Zhu, L. et al. Half of an antipodal spherical design. Arch. Math. 110, 459–466 (2018). https://doi.org/10.1007/s00013-017-1141-1

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Mathematics Subject Classification

  • 05B30
  • 05B35

Keywords

  • Spherical design
  • Leech lattice
  • Antipodal