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Distribution of the points of a design on the sphere. (English. Russian original) Zbl 1106.05020
Izv. Math. 69, No. 5, 1061-1079 (2005); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 69, No. 5, 205-224 (2005).
Author’s abstract: We determine the size of spherical caps with centres at the points of a design that cover the whole sphere in Euclidean space with a given multiplicity. By projecting \(q\)-designs on one-dimensional subspaces, we obtain the nodes of a Chebyshev-type quadrature formula of the same precision \(q\). For large values of \(q\) we establish that the points of a minimal \(q\)-design are uniformly distributed on the sphere. We construct a weighted cubature formula on the sphere with the minimum number of nodes.

05B30 Other designs, configurations
65D32 Numerical quadrature and cubature formulas
05B40 Combinatorial aspects of packing and covering
05E35 Orthogonal polynomials (combinatorics) (MSC2000)
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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