  We give here a detailed description of the latest INPOP planetary ephemerides
INPOP20a. We test the sensitivity of the Sun oblateness determination obtained
with INPOP to different models for the Sun core rotation. We also present new
evaluations of possible GRT violations with the PPN parameters $\beta$,$\gamma$
and $\dot{\mu}/\mu$. With a new method for selecting acceptable alternative
ephemerides we provide conservative limits of about $7.16 \times 10^{-5}$ and
$7.49 \times 10^{-5}$ for $\beta-1$ and $\gamma-1$ respectively using the
present day planetary data samples. We also present simulations of Bepi-Colombo
range tracking data and their impact on planetary ephemeris construction. We
show that the use of future BC range observations should improve these
estimates, in particular $\gamma$. Finally, interesting perspectives for the
detection of the Sun core rotation seem to be reachable thanks to the BC
mission and its accurate range measurements in the GRT frame.
