Packing and Covering with Centrally Symmetric Convex Disks

Given a convex disk K (a convex compact planar set with nonempty interior), let δL(K) and θL(K) denote the lattice packing density and the lattice covering density of K, respectively. We prove that for every centrally-symmetric convex disk K we have that $$ 1\le\delta_L(K)\theta_L(K)\le1.17225\ldots $$ The left inequality is tight and it improves a 10-year old result.

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