Abstract
This note, by studying the relations between the length of the shortest lattice vectors and the covering minima of a lattice, proves that for every d‐dimensional packing lattice of balls one can find a four‐dimensional plane, parallel to a lattice plane, such that the plane meets none of the balls of the packing, provided that the dimension d is large enough. Nevertheless, for certain ball packing lattices, the highest dimension of such ‘free planes’ is far from d.
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