  We present a fully automated implementation of next-to-leading order
electroweak (NLO EW) corrections in the OpenLoops matrix-element generator
combined with the Sherpa and Munich Monte Carlo frameworks. The
process-independent character of the implemented algorithms opens the door to
NLO QCD+EW simulations for a vast range of Standard Model processes, up to high
particle multiplicity, at current and future colliders. As a first application,
we present NLO QCD+EW predictions for the production of positively charged
on-shell W bosons in association with up to three jets at the Large Hadron
Collider. At the TeV energy scale, due to the presence of large Sudakov
logarithms, EW corrections reach the 20-40% level and play an important role
for searches of physics beyond the Standard Model. The dependence of NLO EW
effects on the jet multiplicity is investigated in detail, and we find that
W+multijet final states feature genuinely different EW effects as compared to
the case of W+1jet.
