  We present the resummed predictions for inclusive cross-section for Drell-Yan
(DY) production as well as onshell $Z,W^\pm$ productions at
next-to-next-to-next-to leading logarithmic (N$^{3}$LL) accuracy. Using the
standard techniques, we derive the $N$-dependent coefficients in the Mellin-$N$
space as well as the $N$-independent constants and match the resummed result
through the minimal prescription matching procedure with that of existing
next-to next-to leading order (NNLO). In addition to the standard $\ln N$
exponentiation, we study the numerical impacts of exponentiating
$N$-independent part of the soft function and the complete $\bar{g}_0$ that
appears in the resummed predictions in $N$ space. All the analytical pieces
needed in these different approaches are extracted from the soft-virtual part
of the inclusive cross section known to next-to-next-to-next-to leading order
(N$^3$LO). We perform a detailed analysis on the scale and parton distribution
function (PDF) variations and present predictions for the 13 TeV LHC for the
neutral Drell-Yan process as well as onshell charged and neutral vector boson
productions.
