We aim at producing produce approximate N3LO espressions for all observables used for PDF determination, with the joint goal of providing robust missing higher order uncertainty estimates for NNLO computation, and a first N3LO PDF set.

Current directions of  progress are is in producing combined threshold and transverse momentum resummation, and in extending this at the fully differential level, with rapidity dependence. The evaluation of cross-sections in the high energy limit, either by exploting high-energy (BFKL) resummation, or by direct evaluation of the fixed N3LO result in the high energy limit, are currently being pursued.