  We report on a high-precision calculation of the Bhabha process in Quantum
Electrodynamics, of interest for precise luminosity determination of
electron-positron colliders involved in R measurements in the region of
hadronic resonances. The calculation is based on the matching of exact
next-to-leading order corrections with a Parton Shower algorithm. The accuracy
of the approach is demonstrated in comparison with existing independent
calculations and through a detailed analysis of the main components of
theoretical uncertainty, including two-loop corrections, hadronic vacuum
polarization and light pair contributions. The calculation is implemented in an
improved version of the event generator BABAYAGA with a theoretical accuracy of
the order of 0.1%. The generator is now available for high-precision
simulations of the Bhabha process at flavour factories.
