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In this article we obtain an upper bound for the number of spherical segments of angular radius α that lie without overlapping on the surface of an n-dimensional sphere, and an upper bound for the density of filling n-dimensional euclidean space with equal spheres. In these bounds, the constant in the exponent of n is less than the corresponding constant in previously known bounds. Bibliography: 8 items.
V.M. Sidelnikov (Thu,) studied this question.