Calculation of the [Formula presented] parameter in the static limit

We calculate the [Formula presented] parameter, relevant for [Formula presented]-[Formula presented] mixing, from a lattice gauge theory simulation at [Formula presented]. The bottom quarks are simulated in the static theory, the light quarks with Wilson fermions. Improved smearing functions produced by a variational technique MOST are used to reduce statistical errors and minimize excited-state contamination of the ground-state signal. We obtain [Formula presented] which corresponds to [Formula presented] = [Formula presented] for the one-loop renormalization-scheme-independent parameter. The systematic errors include the uncertainty due to alternative (less favored) treatments of the perturbatively calculated mixing coefficients; this uncertainty is at least as large as residual differences between Wilson-static and clover-static results. Our result agrees with extrapolations of results from relativistic (Wilson) heavy quark simulations.