  We use lattice QCD simulations, with MILC configurations (including vacuum
polarization from u, d, and s quarks), to update our previous determinations of
the QCD coupling constant. Our new analysis uses results from 6 different
lattice spacings and 12 different combinations of sea-quark masses to
significantly reduce our previous errors. We also correct for
finite-lattice-spacing errors in the scale setting, and for nonperturbative
chiral corrections to the 22 short-distance quantities from which we extract
the coupling. Our final result is alpha_V(7.5GeV,nf=3) = 0.2120(28), which is
equivalent to alpha_msbar(M_Z,n_f=5)= 0.1183(8). We compare this with our
previous result, which differs by one standard deviation.
