Geodesic
An estimate of the radius of a~cylinder imbeddable in every lattice packing of $n$-dimensional unit spheres
Matematičeskie zametki, Tome 17 (1975) no. 1, pp. 123-128.

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This note is devoted to the reduction of the problem in the title to a more fully explored problem in the geometry of numbers. The estimates obtained are given in Table 1. 
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S. S. Ryshkov; J. G. Horváth. An estimate of the radius of a~cylinder imbeddable in every lattice packing of $n$-dimensional unit spheres. Matematičeskie zametki, Tome 17 (1975) no. 1, pp. 123-128. http://geodesic.mathdoc.fr/item/MZM_1975_17_1_a14/