Optimal asymptotic bounds for spherical designs
arXiv:1009.4407184 citationsh-index: 14
Originality Highly original
AI Analysis
Settles a long-standing open problem in approximation theory and combinatorial geometry, providing the first proof of existence with optimal order.
Proved the Korevaar-Meyers conjecture that spherical t-designs with N points exist for N ≥ c_d t^d, establishing optimal asymptotic bounds.
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 $d$.