We consider finite lattice ball packings with respect to parametric density and show that densest packings are attained in critical lattices if the number of translates and the density parameter are sufficiently large. A corresponding result is not valid for general centrally symmetric convex bodies.
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The second author was partially supported by a DAAD Postdoc fellowship and the hospitality of Peking University during his work.
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Betke, U., Schürmann, A. Lattices of Optimal Finite Lattice Packings. Monatsh. Math. 144, 31–38 (2005). http://doi.org/10.1007/s00605-004-0262-3
- 2000 Mathematics Subject Classification: 05B40, 11H06, 52C07, 52C17
- Key words: Finite lattice packing, sphere packing, parametric density