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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 β, γ and 
. With a new method for selecting acceptable alternative ephemerides we provide conservative limits of about 7.16 × 10-5 and 7.49 × 10-5 for β-1 and γ-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 γ. 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.
