Geodesic
Maximal packing density of $n$-dimensional Euclidean space with equal balls
Matematičeskie zametki, Tome 18 (1975) no. 2, pp. 301-311.

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An estimate $\delta_n\le2^{-n(0,\!5237+o(1))}$ is obtained for the maximal packing density of $n$-dimensional Euclidean space with equal balls for $n\to\infty$. 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. 
@article{MZM_1975_18_2_a15,
     author = {V. I. Levenshtein},
     title = {Maximal packing density of $n$-dimensional {Euclidean} space with equal balls},
     journal = {Matemati\v{c}eskie zametki},
     pages = {301--311},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_2_a15/}
}
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V. I. Levenshtein. Maximal packing density of $n$-dimensional Euclidean space with equal balls. Matematičeskie zametki, Tome 18 (1975) no. 2, pp. 301-311. http://geodesic.mathdoc.fr/item/MZM_1975_18_2_a15/