2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68290We show that for every lattice packing of $n$-dimensional spheres there exists an $(n/\log_2(n))$-dimensional affine plane which does not meet any of the spheres in their interior, provided $n$ is large enough. Such an affine plane is called a free plane and our result improves on former bounds.7 pagesMetric Geometry52C17; 11H31text