  Modern astrometry is based on angular measurements at the micro-arcsecond
level. At this accuracy a fully general relativistic treatment of the data
reduction is required. This paper concludes a series of articles dedicated to
the problem of relativistic light propagation, presenting the final
microarcsecond version of a relativistic astrometric model which enable us to
trace back the light path to its emitting source throughout the non-stationary
gravity field of the moving bodies in the Solar System. The previous model is
used as test-bed for numerical comparisons to the present one. Here we also
test different versions of the computer code implementing the model at
different levels of complexity to start exploring the best trade-off between
numerical efficiency and the micro-arcsecond accuracy needed to be reached.
