Refined Big Bang Nucleosynthesis Constraints on $\Omega_{Baryon}$ and $N_{\nu}$

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.