Accurate Determinations of $\alpha_s$ from Realistic Lattice QCD

We present a new determination of the QCD coupling constant from lattice QCD simulations combined with experimental data about mass spectra. The analysis presented here is the first in lattice QCD to: 1) include vacuum polarization effects from all three light-quark flavors in the simulations; 2) include third-order terms in perturbation theory; 3) systematically estimate fourth and higher-order terms; 4) use an unambiguous determiniation of the lattice spacing; and 5) use $\order(a^2)$-accurate actions for gluons and light quarks. We use 28 different (but related) short-distance quantities to obtain a final value of $\alpha_{\bar{\mathrm{MS}}}^{(5)}(M_Z) = 0.1177(13)$