Geodesic
Five Dimensional Non-Lattice Sphere Packings
Canadian mathematical bulletin, Tome 10 (1967) no. 3, pp. 387-393

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The densest lattice packings of spheres in Euclidean spaces En of n dimensions are known for n ≤ 8 (for full n — references see [6]). However, it i s not known for any n ≥ 3 whether there can be any non-lattice sphere packing with density exceeding that of the corresponding densest lattice packing. 
Leech, John. Five Dimensional Non-Lattice Sphere Packings. Canadian mathematical bulletin, Tome 10 (1967) no. 3, pp. 387-393. doi: 10.4153/CMB-1967-037-5
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     author = {Leech, John},
     title = {Five {Dimensional} {Non-Lattice} {Sphere} {Packings}},
     journal = {Canadian mathematical bulletin},
     pages = {387--393},
     year = {1967},
     volume = {10},
     number = {3},
     doi = {10.4153/CMB-1967-037-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1967-037-5/}
}
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