  We present a new lower bound on the Bowen-Radin maximal density of radius-R
ball packings in the m-dimensional hyperbolic space, improving on the basic
covering bound by factor \Omega(m(R+\ln m)) as m tends to infinity. This is
done by applying the recent theorem of Campos, Jenssen, Michelen and
Sahasrabudhe on independent sets in graphs with sparse neighbourhoods.
