Geodesic
Distribution of the points of a~design on the sphere
Izvestiya. Mathematics , Tome 69 (2005) no. 5, pp. 1061-1079.

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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. 
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V. A. Yudin. Distribution of the points of a~design on the sphere. Izvestiya. Mathematics , Tome 69 (2005) no. 5, pp. 1061-1079. http://geodesic.mathdoc.fr/item/IM2_2005_69_5_a7/

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