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 Mat. Sb. (N.S.), 1974, Volume 95(137), Number 1(9), Pages 148–158 (Mi msb3749)

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

V. M. Sidel'nikov

Abstract: 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.
Bibliography: 8 titles.

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English version:
Mathematics of the USSR-Sbornik, 1974, 24:1, 147–157

Bibliographic databases:

UDC: 513.82
MSC: 52A45

Citation: V. M. Sidel'nikov, “New bounds for densest packing of spheres in $n$-dimensional Euclidean space”, Mat. Sb. (N.S.), 95(137):1(9) (1974), 148–158; Math. USSR-Sb., 24:1 (1974), 147–157

Citation in format AMSBIB
\Bibitem{Sid74} \by V.~M.~Sidel'nikov \paper New bounds for densest packing of spheres in $n$-dimensional Euclidean space \jour Mat. Sb. (N.S.) \yr 1974 \vol 95(137) \issue 1(9) \pages 148--158 \mathnet{http://mi.mathnet.ru/msb3749} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=362060} \zmath{https://zbmath.org/?q=an:0308.52013} \transl \jour Math. USSR-Sb. \yr 1974 \vol 24 \issue 1 \pages 147--157 \crossref{https://doi.org/10.1070/SM1974v024n01ABEH001911} 

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This publication is cited in the following articles:
1. B. S. Kashin, “Diameters of some finite-dimensional sets and classes of smooth functions”, Math. USSR-Izv., 11:2 (1977), 317–333
2. Eiichi Bannai, “On the Weight Distribution of Spherical t-designs”, European Journal of Combinatorics, 1:1 (1980), 19
3. L. Danzer, “Finite point-sets on S2 with minimum distance as large as possible”, Discrete Mathematics, 60 (1986), 3
4. A. Neumaier, J.J. Seidel, “Discrete measures for spherical designs, eutactic stars and lattices”, Indagationes Mathematicae (Proceedings), 91:3 (1988), 321
5. G Fazekas, V.I Levenshtein, “On upper bounds for code distance and covering radius of designs in polynomial metric spaces”, Journal of Combinatorial Theory, Series A, 70:2 (1995), 267
6. P. Delsarte, V.I. Levenshtein, “Association schemes and coding theory”, IEEE Trans Inform Theory, 44:6 (1998), 2477
7. Dorofeev, AY, “Matrix groups related to the quaternion group and spherical orbit codes”, Designs Codes and Cryptography, 37:3 (2005), 391
8. Sho Suda, “On spherical designs obtained from Q-polynomial association schemes”, J. Combin. Designs, 2011, n/a
9. N. O. Kotelina, A. B. Pevnyi, “Sidelnikov inequality”, St. Petersburg Math. J., 26:2 (2015), 351–356
10. N. O. Kotelina, A. B. Pevnyi, “Complex spherical semi-designs”, Russian Math. (Iz. VUZ), 61:5 (2017), 46–51
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