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Matematicheskie Zametki, 1975, Volume 18, Issue 2, Pages 301–311 (Mi mzm7653)  
This article is cited in 7 scientific papers (total in 7 papers)

Maximal packing density of n-dimensional Euclidean space with equal balls

V. I. Levenshtein

Applied Mathematics Institute, Academy of Sciences of the USSR
Full-text PDF (749 kB) Citations (7)
Abstract: An estimate δn⩽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.
Received: 25.03.1974
English version:
Mathematical Notes, 1975, Volume 18, Issue 2, Pages 765–771
DOI: https://doi.org/10.1007/BF01818046
Bibliographic databases:
UDC: 513.82
Language: Russian
Citation: V. I. Levenshtein, “Maximal packing density of n-dimensional Euclidean space with equal balls”, Mat. Zametki, 18:2 (1975), 301–311; Math. Notes, 18:2 (1975), 765–771
Citation in format AMSBIB
\Bibitem{Lev75}
\by V.~I.~Levenshtein
\paper Maximal packing density of $n$-dimensional Euclidean space with equal balls
\jour Mat. Zametki
\yr 1975
\vol 18
\issue 2
\pages 301--311
\mathnet{http://mi.mathnet.ru/mzm7653}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=397565}
\zmath{https://zbmath.org/?q=an:0315.52017}
\transl
\jour Math. Notes
\yr 1975
\vol 18
\issue 2
\pages 765--771
\crossref{https://doi.org/10.1007/BF01818046}
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  • https://www.mathnet.ru/eng/mzm7653
  • https://www.mathnet.ru/eng/mzm/v18/i2/p301
    • This publication is cited in the following 7 articles:
    1. Aleksandr Vasilevich Malyshev, “Osnovnye ponyatiya i teoremy geometrii chisel”, Chebyshevskii Sbornik, 20:3 (2020), 44  crossref
    2. A. V. Malyshev, “Osnovnye ponyatiya i teoremy geometrii chisel”, Chebyshevskii sb., 20:3 (2019), 43–73  mathnet  crossref
    3. Henry Cohn, Yufei Zhao, “Sphere packing bounds via spherical codes”, Duke Math. J., 163:10 (2014)  crossref
    4. Combinatorial Geometry, 1995, 319  crossref
    5. L. Danzer, “Finite point-sets on S2 with minimum distance as large as possible”, Discrete Mathematics, 60 (1986), 3  crossref
    6. G. Fejes Tóth, Convexity and Its Applications, 1983, 318  crossref
    7. Peter M. Gruber, Contributions to Geometry, 1979, 186  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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