  We present here the results of our high accuracy simulations of $q\bar q$
potential in $d=4$ SU(3) Yang-Mills theory. We measure this quantity by
measuring the {\it Polyakov Loop Correlators} using the {\it exponential
variance reduction technique(multilevel)} of Luscher and Weisz. We further use
numerical integration of the one-link integrals of SU(3) theory by adopting
techniques proposed by de Forcrand and Roiesnell achieving significant speed-up
in the process. Measurements were done at $\beta = 5.7$ on $24^3x32$ as well as
$32^4$ lattices for separations between the Polyakov loops in the range $r =
2-9$ in lattice units. We analyse the results in terms of the force between
$q\bar q$ pair as well as in terms of a {\em scaled second derivative} of the
potential. We show that the data is accurate enough to distinguish between
different string models and that it seems to favour the expression for ground
state energy of a Nambu-Goto string. We conclude by discussing future plans.
