  The recent work by Iha et al shows an upper bound on mass anomalous dimension
$\gamma_m$ of multi-flavor massless QCD at the renormalization group fixed
point from the conformal bootstrap in $SU(N_F)_V$ symmetric conformal field
theories under the assumption that the fixed point is realizable with the
lattice regularization based on staggered fermions. We show that the almost
identical but slightly stronger bound applies to the regularization based on
Wilson fermions (or domain wall fermions) by studying the conformal bootstrap
in $SU(N_f)_L \times SU(N_f)_R$ symmetric conformal field theories. For
$N_f=8$, our bound implies $\gamma_m < 1.31$ to avoid dangerously irrelevant
operators that are not compatible with the lattice symmetry.
