  The search for new interactions and particles in high-energy collider physics
relies on precise background predictions. This has led to many advances in
combining precise fixed-order cross-section calculations with detailed event
generator simulations. In recent years, fixed-order QCD calculations of
inclusive cross sections at N3LO precision have emerged, followed by an
impressive progress at producing differential results. Once differential
results become publicly available, it would be prudent to embed these into
event generators to allow the community to leverage these advances. This note
offers some concrete thoughts on ME+PS matching at third order in QCD. As a
method for testing these thoughts, a toy calculation of $e^+e^-\rightarrow u
\bar u$ at $\mathcal{O}(\alpha_s^3)$ is constructed, and combined with an event
generator through unitary matching. The toy implementation may serve also as
blueprint for high-precision QCD predictions at future lepton colliders. As a
byproduct of the N3LO matching formula, a new NNLO+PS formula for processes
with "additional" jets is obtained.
