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In this paper we prove that no packing of unit balls in Euclidean space $\mathbb{R}^8$ has density greater than that of the $E_8$-lattice packing.
H. Petersson
1932
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H. Rademacher and H. S. Zuckerman
1938
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L. Fejes Tóth
1943
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M. Abramowitz, I. Stegun
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P. Delsarte
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P. Delsarte, J. M. Goethals, and J. J. Seidel
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G. A. Kabatiansky and V. I. Levenshtein
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D. Hejhal
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D. Mumford
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J. H. Conway and N. J. A. Sloane
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V. A. Yudin
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J. Bruinier
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H. Cohn, N. Elkies
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F. Pfender, G. M. Ziegler,
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T. Hales
2005
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H. Cohn, A. Kumar
2007
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D. Zagier
2008
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A. Bondarenko, D. Radchenko, M. Viazovska
2013
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