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We prove a lower bound of $\Omega (d^{3/2} \cdot (2/\sqrt{3})^d)$ on the kissing number in dimension $d$.
H. Minkowski, Diskontinuitätsbereich für arithmetische Äquivalenz , J. Reine Angew. Math. 129
1905
Earlier work this paper cites.
H. Davenport and C. A. Rogers, Hlawka’s theorem in the geometry of numbers , Duke Math. J. 14
1947
Earlier work this paper cites.
C. A. Rogers, Existence theorems in the geometry of numbers , Ann. of Math. 48
1947
Earlier work this paper cites.
E. N. Gilbert, A comparison of signalling alphabets , Bell System Tech. J. 31
1952
Earlier work this paper cites.
K. Schütte and B. L. van der Waerden, Das Problem der dreizehn Kugeln , Math. Ann. 125
1952
Earlier work this paper cites.
C. Chabauty, Résultats sur l’empilement de calottes égales sur une périsphère de R n R^{n} et correction à un travail antérieur , C. R. Acad. Sci. Paris 236
1953
Earlier work this paper cites.
R. A. Rankin, The closest packing of spherical caps in n n dimensions , Proc. Glasgow Math. Assoc. 2
1955
Earlier work this paper cites.
R. R. Varshamov, Estimate of the number of signals in error correcting codes , Dokl. Akad. Nauk SSSR 117
1957
Earlier work this paper cites.
H. S. M. Coxeter, L. Few, and C. A. Rogers, Covering space with equal spheres , Mathematika 6
1959
Earlier work this paper cites.
C. E. Shannon, Probability of error for optimal codes in a Gaussian channel , Bell System Tech. J. 38
1959
Earlier work this paper cites.
A. D. Wyner, Capabilities of bounded discrepancy decoding , Bell Systems Tech. J. 44
1965
Earlier work this paper cites.
P. Delsarte, Bounds for unrestricted codes, by linear programming , Philips Res. Rep. 27
1972
Cited alongside, same era.
G. A. Kabatjanskiĭ and V. I. Levenšteĭn, Bounds for packings on the sphere and in space , Problemy Peredači Informacii 14
1978
Cited alongside, same era.
V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space , Soviet Math. Dokl. 20
1979
Cited alongside, same era.
A. M. Odlyzko and N. J. A. Sloane, New bounds on the number of unit spheres that can touch a unit sphere in n n dimensions , J. Combin. Theory Ser. A 26
1979
Cited alongside, same era.
K. Ball, A lower bound for the optimal density of lattice packings , Int. Math. Res. Not. 1992
1992
Cited alongside, same era.
M. Krivelevich, S. Litsyn, and A. Vardy, A lower bound on the density of sphere packings via graph theory , Int. Math. Res. Not. 2004
2004
Later among the works it cites.
F. Pfender and G. M. Ziegler, Kissing numbers, sphere packings, and some unexpected proofs , Notices Amer. Math. Soc. 51
2004
Later among the works it cites.
O. R. Musin, The kissing number in four dimensions , Ann. of Math. 168
2008
Later among the works it cites.
S. Vance, Improved sphere packing lower bounds from Hurwitz lattices , Adv. Math. 227
2011
Later among the works it cites.
P. Boyvalenkov, S. Dodunekov, and O. Musin, A survey on the kissing numbers , Serdica Math. J. 38
2012
Later among the works it cites.
A. Venkatesh, A note on sphere packings in high dimension , Int. Math. Res. Not. 2013
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1998
Cited alongside, same era.
J. H. Conway and N. J. A. Sloane, Sphere packings, lattices and groups , third ed., vol. 290, Springer, 1999
1999
Cited alongside, same era.
H. Cohn and Y. Zhao, Sphere packing bounds via spherical codes , Duke Math. J. 163
2002
Cited alongside, same era.
K. Böröczky, Finite packing and covering , vol. 154, Cambridge University Press, 2004
2004
Cited alongside, same era.
T. Jiang and A. Vardy, Asymptotic improvement of the Gilbert-Varshamov bound on the size of binary codes , IEEE Trans. Inform. Theory 50
2004
Cited alongside, same era.
2013
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H. Cohn, Packing, coding, and ground states , arXiv:1603.05202 (2016)
2016
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2017
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E. Davies, M. Jenssen, W. Perkins, and B. Roberts, On the average size of independent sets in triangle-free graphs , Proc. Amer. Math. Soc. 146
2018
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