“…For
the best lower bound is due to Lefmann [
9]:
which is a logarithmic improvement over a bound by Bertram‐Kretzberg, Hofmeister, and Lefmann [
3]. A simple probabilistic argument gives the following lower bound for arbitrary
:
see [
10] for a proof. It seems likely that one should be able to improve (6) by a logarithmic factor similarly to (5) but we do not pursue this direction here.…”