# Relation between spherical designs through a Hopf map

@article{Okuda2015RelationBS, title={Relation between spherical designs through a Hopf map}, author={Takayuki Okuda}, journal={arXiv: Metric Geometry}, year={2015} }

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 $S^1$.

## 2 Citations

### Design Theory from the Viewpoint of Algebraic Combinatorics

- MathematicsGraphs and Combinatorics
- 2016

We give a survey on various design theories from the viewpoint of algebraic combinatorics. We will start with the following themes. The similarity between spherical t-designs and combinatorial…

### Design Theory from the Viewpoint of Algebraic Combinatorics

- MathematicsGraphs Comb.
- 2017

This study proposes to study t-designs in each shell of these classical P- and Q-polynomial association schemes, in general, each shell is not Q- polynomial.

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