by Henk, Martin, Ziegler, Günter M., Zong, Chuanming.
Series: 2000-04, Preprints
This note, by studying relations between the length
of shortest lattice vectors and the covering minima of a lattice,
mainly proves that for every $d$-dimensional packing lattice of balls
one can find a $4$-dimensional plane, parallel to a lattice plane,
such that the plane meets none of the balls of the packing, provided the
dimension $d$ is large enough. On the other hand, we show that for
certain ball packing lattices
the highest dimension of such ``free planes'' is far from $d$.
covering minima, homogeneous