In this work, we present the extension of an alternative subtraction scheme
for next-to-leading order QCD calculations to the case of an arbitrary number
of massless final-state partons. The scheme is based on the splitting kernels
of an improved parton shower and comes with a reduced number of final state
momentum mappings. While a previous publication including the setup of the
scheme has been restricted to cases with maximally two massless partons in the
final state, we here provide the final state real emission and integrated
subtraction terms for processes with any number of massless partons. We apply
our scheme to three jet production at lepton colliders at next-to-leading order
and present results for the differential C parameter distribution.Comment: 45 pages, 5 figures v2: several references added; v3: title changed,
references and a discussion of further scaling improvement added. Corresponds
to published journal versio