NNNLO soft-gluon corrections for the top-antitop pair production cross section

I present a calculation of next-to-next-to-next-to-leading-order (NNNLO) soft-gluon corrections for top-antitop pair production in hadronic collisions. Approximate NNNLO (aNNNLO) results are obtained by adding the NNNLO soft-gluon corrections to the complete next-to-next-to-leading-order (NNLO) cross section. Theoretical predictions are shown for the total aNNNLO $t\bar{t}$ cross section at LHC and Tevatron energies. The aNNNLO cross sections are larger but have smaller theoretical uncertainties than at NNLO.