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I present theoretical calculations of $t{\bar t}$ production cross sectionsthrough aN$^3$LO in proton-proton collisions. I show that soft-gluoncorrections dominate the perturbative expansion not only for LHC energies butalso for future collider energies through 100 TeV. Detailed results arepresented for various collision energies. The $K$-factors are large andincrease slowly with increasing energy. The scale uncertainties decreasegreatly as we move to higher perturbative orders.

Higher-order corrections for $t{\bar t}$ production at high energies