Abstract
ABSTRACTRogers proved in a constructive way that every packing lattice Λ of a symmetric convex body K in is contained in a packing lattice whose covering radius is less than 3. By a slight modification of Rogers’ approach better bounds for lp-balls are obtained. Together with Rogers’ constructive proof, this leads, for instance, to a simple o(nn/2) running time algorithm that refines successively the packing lattice Dn (checkboard lattice) of the unit ball Bn and terminates with a packing lattice with density . We have also implemented this algorithm and in small dimensions (⩽ 25) and for certain simple structured start lattices like or Dn the algorithm often terminates with packing lattices achieving the best-known lattice densities.
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