We present here the results of our high accuracy simulations of $qbar q$ 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 $qbar q$ 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.
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