New bounds for densest packing of spheres in $n$-dimensional Euclidean space

In this article we obtain an upper bound for the number of spherical segments of angular radius $\alpha$ 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.
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