  Information of the phase structure of many flavor SU(3) gauge theory is of
great interest for finding a theory which dynamically breaks the electro-weak
symmetry. We study the SU(3) gauge theory with fermions for $N_f=12$ and 16 in
fundamental representation. Both of them, through perturbation theory, reside
in the conformal phase. We try to determine the phase of each theory
non-perturbatively with lattice simulation and to find the characteristic
behavior of the physical quantities in the phase. HISQ type staggered fermions
are used to reduce the discretization error which could compromise the behavior
of the physical quantity to determine the phase structure at non-zero lattice
spacings. Spectral quantities such as bound state masses of meson channel and
meson decay constants are investigated with careful finite volume analysis. Our
data favor the conformal over chiral symmetry breaking scenario for both
$N_f=12$ and 16.
