  Lattice work, exploring the Higgs mass triviality bound, seems to indicate
that a strongly interacting scalar sector in the minimal standard model cannot
exist while low energy QCD phenomenology seems to indicate that it could. We
attack this puzzle using the 1/N expansion and discover a simple criterion for
selecting a lattice action that is more likely to produce a heavy Higgs
particle. Our large $N$ calculation suggests that the Higgs mass bound might be
around $850 GeV$, which is about 30% higher than previously obtained.
