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Lattices in the sense of discrete subgroups of Euclidean spaces, as used in number theory, discrete geometry, Lie groups, etc. (Not to be confused with lattice theory or lattices as used in physics! For lattices (ordered sets), use the tag: [lattice-theory])
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Techniques for showing optimality of given packing
My knowledge is limited when it comes to general combinatorial packings. But the kind of problem OP described is important in coding theory, where the difference between proving the existence of a goo …