• Corpus ID: 119576950

Relation between spherical designs through a Hopf map

  title={Relation between spherical designs through a Hopf map},
  author={Takayuki Okuda},
  journal={arXiv: Metric Geometry},
  • T. Okuda
  • Published 28 June 2015
  • Mathematics
  • arXiv: Metric Geometry
Cohn--Conway--Elkies--Kumar [Experiment. Math. (2007)] described that one can construct a family of designs on $S^{2n-1}$ from a design on $\mathbb{CP}^{n-1}$. In this paper, we prove their claim for the case where $n=2$. That is, we give an algorithm to construct $2t$-designs on $S^{3}$ as products through a Hopf map $S^3 \rightarrow S^2$ of a $t$-design on $S^2$ and a $2t$-design on $S^1$. 
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