# Optimal asymptotic bounds for spherical designs

@article{Bondarenko2010OptimalAB,
title={Optimal asymptotic bounds for spherical designs},
author={Andriy V. Bondarenko and Danylo V. Radchenko and Maryna S. Viazovska},
journal={arXiv: Metric Geometry},
year={2010}
}
• Published 22 September 2010
• Mathematics
• arXiv: Metric Geometry
In this paper we prove the conjecture of Korevaar and Meyers: for each $N\ge c_dt^d$ there exists a spherical $t$-design in the sphere $S^d$ consisting of $N$ points, where $c_d$ is a constant depending only on $d$.
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This work applies polynomial techniques to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality and proposes new upper bounds due to Fazekas and Levenshtein.
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