  We calculate the triviality bound on the Higgs mass in scalar field theory
models whose global symmetry group $SU(2)_L \times SU(2)_{\rm custodial}
\approx O(4)$ has been replaced by $O(N)$ and $N$ has been taken to infinity.
Limits on observable cutoff effects at four percent in several regularized
models with tunable couplings in the bare action yield triviality bounds
displaying a large degree of universality. Extrapolating from $N=\infty$ to
$N=4$ we conservatively estimate that a Higgs particle with mass up to
$0.750~TeV$ and width up to $0.290~TeV$ is realizable without large cutoff
effects, indicating that strong scalar self interactions in the standard model
are not ruled out.
  Note: The full ps file of this preprint is also available via anonymous ftp
to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for
username "anonymous" and for password your name. The file is in the directory
pub/vranas (to go to that directory type: cd pub/vranas) and is called
lrg_n_hig.ps (to get it type: get lrg_n_hig.ps)
