An estimate δ n ⩽ 2-n(0.5237+o(1)) is obtained for the maximal packing density of n-dimensional Euclidean space with equal balls for n→ ∞. This result is based on an improvement in a corresponding upper estimate for the maximal packing density of the unit (n-1)-dimensional sphere with spherical caps of fixed angular radius.
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Translated from Matematicheskie Zametki, Vol. 18, No. 2, pp. 301–311, August, 1975.
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Levenshtein, V.I. Maximal packing density of n-dimensional Euclidean space with equal balls. Mathematical Notes of the Academy of Sciences of the USSR 18, 765–771 (1975). https://doi.org/10.1007/BF01818046
- Euclidean Space
- Packing Density
- Dimensional Sphere
- Maximal Packing
- Equal Ball