  We include correlations between elemental abundances in a Monte Carlo
statistical analysis of BBN predictions, which, along with updated reaction
rates and an improved BBN code, lead to tightened constraints on $\Omega_{B}$
and $N_{\nu}$. Observational upper limits on the primordial \he and $\rm {D +
{^3He}}$ fractions of $24 \%$ (by weight) and $ 10^{-4}$ respectively lead to
the limits: $0.015 \le \Omega_{B} \le 0.070$, and $N_{\nu} \le 3.04$. The
former limit appears to be incompatible with purely baryonic galactic halo dark
matter, while the latter puts qualitatively new constraints on neutrinos, and
physics beyond the standard model.
