2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70103Using graph-theoretic methods we give a new proof that for all sufficiently large $n$, there exist sphere packings in $\R^n$ of density at least $cn2^{-n}$, exceeding the classical Minkowski bound by a factor linear in $n$. This matches up to a constant the best known lower bounds on the density of sphere packings due to Rogers, Davenport-Rogers, and Ball. The suggested method makes it possible to describe the points of such a packing with complexity $\exp(n\log n)$, which is significantly lower than in the other approaches.6 pages, 2 postscript figuresCombinatoricsMetric Geometry05C90, 52C17 (Primary) 05C69, 11H31 (Secondary)text