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.
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