We report on updated precision predictions for total cross sections of coloured supersymmetric particle production at the LHC with a centre-of-mass energy of $\sqrt S$ = 13.6 TeV, computed with the modern PDF4LHC21 set. The cross sections are calculated at an approximated NNLO accuracy in QCD and contain corrections from the threshold resummation of soft-gluon emission up to NNLL accuracy as well as Coulomb-gluon contributions including bound-state terms. The corrections are found to increase the cross sections and reduce the theoretical uncertainty as compared to the best available fixed-order calculations. These predictions constitute the state-of-the-art calculations and update the existing results for $\sqrt S$ = 13 TeV. We make our new results publicly available in the version 2.0 update to the code package NNLL-fast.
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