Antenna subtraction for final-state radiation at N$^3$LO

I review some aspects of antenna subtraction at next-to-next-to-leading order (NNLO) in QCD and provide motivation for its extension to N$^3$LO. Next, I introduce the antenna functions required for the construction of infrared counterterms for final-state radiation at this order. Lastly, I describe the evaluation of the antenna functions and their phase-space integration, first presented in [1]-[3], and I elaborate on their application to precision observables in jet production at lepton colliders.