  Quasi-elastic (QEL) scattering measurements have been performed using
$^{28}$Si projectile off a $^{90}$Zr target at energies around the Coulomb
barrier. A Bayesian analysis within the framework of coupled channels (CC)
calculations is performed in a large parameter space of quadrupole and
hexadecapole deformations ($\beta_{2}$ and $\beta_{4}$) of $^{28}$Si. Our
results clearly show that $^{28}$Si is an oblate shaped nucleus with
$\beta_{2}$=-$0.38 \pm 0.01$ which is in excellent agreement with
electromagnetic probes. A precise value of hexadecapole deformation for
$^{28}$Si, $\beta_{4}$=+$0.03 \pm 0.01$, along with a consistent value of
quadrupole deformation has now been determined for the first time using QEL
scattering. A remarkable agreement between the experimental $\beta_{4}$ value
of $^{28}$Si and Skyrme-Hartree-Fock based calculations is obtained. The QEL
results obtained previously for $^{24}$Mg (prolate) and the present result for
$^{28}$Si (oblate) hereby affirm the strong sensitivity of the quasi-elastic
scattering to ground state deformations, thus reinforcing its suitability as a
potential probe for rare exotic nuclei.
