  Computations of higher-order QCD corrections for processes with exclusive
final states require a subtraction method for real-radiation contributions. We
present the first-ever generalisation of a subtraction method for third-order
(N3LO) QCD corrections. The Projection-to-Born method is used to combine
inclusive N3LO coefficient functions with an exclusive second-order (NNLO)
calculation for a final state with an extra jet. The input requirements,
advantages, and potential applications of the method are discussed, and
validations at lower orders are performed. As a test case, we compute the N3LO
corrections to kinematical distributions and production rates for single-jet
production in deep inelastic scattering in the laboratory frame, and compare
them with data from the ZEUS experiment at HERA. The corrections are small in
the central rapidity region, where they stabilize the predictions to sub
per-cent level. The corrections increase substantially towards forward rapidity
where large logarithmic effects are expected, thereby yielding an improved
description of the data in this region.
