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Optimal asymptotic bounds for spherical designs. (English) Zbl 1270.05026
Summary: In this paper we prove the conjecture of J. Korevaar and J. L. H. Meyers [Integral Transforms Spec. Funct. 1, No. 2, 105–117 (1993; Zbl 0823.41026)]: for each \(N\geq c_dt^d\), there exists a spherical \(t\)-design in the sphere \(S^d\) consisting of \(N\) points, where \(c_d\) is a constant depending only on \(d\).

MSC:
05B30 Other designs, configurations
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References:
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