  These proceedings describe a computation of the large-$n_f$ terms
contributing to the QCD splitting functions at the fourth order in the strong
coupling constant $\alpha_s$. Using the FORCER package for the reduction of
four-loop two-point Feynman integrals, Mellin moments of the four-loop
splitting functions have been computed. These moments are used to derive
analytic Mellin-space expressions, by forming and finding solutions to systems
of Diophantine equations. Expressions for the terms proportional to $n_f^3$ of
the flavour singlet, and to $n_f^2$ of the flavour non-singlet splitting
functions have been determined.
