  We report on a high-precision calculation of the Bhabha process in QED, of
interest for precise luminosity determination of low-energy electron-positron
colliders. The calculation is based on the matching of exact next-to-leading
order corrections with a Parton Shower algorithm. The structure of the
algorithm (implemented in an improved version of the event generator BABAYAGA)
is illustrated, with a discussion on the resulting theoretical uncertainty, of
the order of 0.1 %.
