Matematičeskie zametki, Tome 18 (1975) no. 2, pp. 301-311
Citer cet article
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/
@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},
year = {1975},
volume = {18},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_2_a15/}
}
TY - JOUR
AU - V. I. Levenshtein
TI - Maximal packing density of $n$-dimensional Euclidean space with equal balls
JO - Matematičeskie zametki
PY - 1975
SP - 301
EP - 311
VL - 18
IS - 2
UR - http://geodesic.mathdoc.fr/item/MZM_1975_18_2_a15/
LA - ru
ID - MZM_1975_18_2_a15
ER -
%0 Journal Article
%A V. I. Levenshtein
%T Maximal packing density of $n$-dimensional Euclidean space with equal balls
%J Matematičeskie zametki
%D 1975
%P 301-311
%V 18
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1975_18_2_a15/
%G ru
%F MZM_1975_18_2_a15
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.
