Geodesic
Six and Seven Dimensional Non-Lattice Sphere Packings
Canadian mathematical bulletin, Tome 12 (1969) no. 2, pp. 151-155

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The densest lattice packings of equal spheres in Euclidean spaces En of n dimensions are known for n ⩽ 8. However, it is not known for any n ⩾ 3 whether there can be any non-lattice sphere packing with density exceeding that of the densest lattice packing. W. Barlow described [1] a non-lattice packing in E3 with the same density as the densest lattice packing, and I described [6] three non-lattice packings in E5 which also have this property. 
Leech, John. Six and Seven Dimensional Non-Lattice Sphere Packings. Canadian mathematical bulletin, Tome 12 (1969) no. 2, pp. 151-155. doi: 10.4153/CMB-1969-014-1
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     author = {Leech, John},
     title = {Six and {Seven} {Dimensional} {Non-Lattice} {Sphere} {Packings}},
     journal = {Canadian mathematical bulletin},
     pages = {151--155},
     year = {1969},
     volume = {12},
     number = {2},
     doi = {10.4153/CMB-1969-014-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-014-1/}
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