  We discuss cross sections for $tW$ production in proton-proton collisions
with energies of up to 100 TeV. We find that, remarkably, the soft-gluon
corrections are numerically dominant even at very high collider energies. We
present results with soft-gluon corrections at approximate NNLO and approximate
N$^3$LO matched to complete NLO results. These higher-order corrections are
large and need to be included for better theoretical accuracy and smaller scale
dependence. Total cross sections as well as top-quark transverse-momentum and
rapidity distributions are presented using various recent sets of parton
distribution functions.
