  We propose a viable theory based on the $SU(3)_C\times SU(3)_L\times U(1)_X$
gauge group supplemented by the $S_4$ discrete group together with other
various symmetries, whose spontaneous breaking gives rise to the current SM
fermion mass and mixing hierarchy. In the proposed theory the small light
active neutrino masses are generated from a linear seesaw mechanism mediated by
three Majorana neutrinos. The model is capable of reproducing the experimental
values of the physical observables of both quark and lepton sectors. Our model
is predictive in the quark sector having 9 effective parameters that allow to
successfully reproduce the four CKM parameters and the six Standard Model (SM)
quark masses. In the SM quark sector, there is particular scenario, motivated
by naturalness arguments, which allows a good fit for its ten observables, with
only six effective parameters. We also study the single heavy scalar production
via gluon fusion mechanism at proton-proton collider. Our model is also
consistent with the experimental constraints arising from the Higgs diphoton
decay rate.
