  Evidence for a flavor asymmetry between the $\bar u$ and $\bar d$ quark
distributions in the proton has been found in deep-inelastic scattering and
Drell-Yan experiments. The pronounced dependence of this flavor asymmetry on
$x$ (fraction of nucleon momentum carried by partons) observed in the Fermilab
E866 Drell-Yan experiment suggested a drop of the $\bar d\left(x\right) / \bar
u\left(x\right)$ ratio in the $x > 0.15$ region. We report results from the
SeaQuest Fermilab E906 experiment with improved statistical precision for $\bar
d\left(x\right) / \bar u\left(x\right)$ in the large $x$ region up to $x=0.45$
using the 120 GeV proton beam. Two different methods for extracting the
Drell-Yan cross section ratios, $\sigma^{pd} /2 \sigma^{pp}$, from the SeaQuest
data give consistent results. The $\bar{d}\left(x\right) /
\bar{u}\left(x\right)$ ratios and the $\bar d\left(x\right) - \bar
u\left(x\right)$ differences are deduced from these cross section ratios for
$0.13 < x < 0.45$. The SeaQuest and E866/NuSea $\bar{d}\left(x\right) /
\bar{u}\left(x\right)$ ratios are in good agreement for the $x\lesssim 0.25$
region. The new SeaQuest data, however, show that $\bar d\left(x\right)$
continues to be greater than $\bar u\left(x\right)$ up to the highest $x$ value
($x = 0.45$). The new results on $\bar{d}\left(x\right) /
\bar{u}\left(x\right)$ and $\bar{d}\left(x\right) - \bar{u}\left(x\right)$ are
compared with various parton distribution functions and theoretical
calculations.
