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By making use of the supplementary advances of the perihelia provided by INPOP10a and INPOP15a (France) and EPM2011 (Russia) ephemerides, we obtain improved Solar System bounds on the cosmologically viable $f(\mathcal{G})$ gravity, where $f$ is an arbitrary function of the Gauss-Bonnet invariant $\mathcal{G}$ . When we estimate new bounds on its model parameters, we consider the Lense-Thirring effect caused by the Sun's angular momentum and the uncertainty of the Sun's quadrupole moment, neither of which were included in related works before. The bounds we obtain in the present work are tighter than the previous ones by at least 5 orders of magnitude. [ABSTRACT FROM AUTHOR]