  We study quenched disordered polymerized membranes in their flat phase by
means of a three-loop perturbative analysis performed in dimension $D =
4-\epsilon$. We derive the renormalization group equations at this order and
solve them up to order $\epsilon^3$. Our results confirm those obtained by
Coquand et al. within a nonperturbative approach [Phys. Rev. E 97, 030102(R)
(2018)] predicting a finite-temperature, finite-disorder wrinkling transition
and those obtained by Coquand and Mouhanna within a recent two-loop order
approach [Phys. Rev. E 103, L031001 (2021)], while correcting some of the
results obtained in this last reference. We compute the anomalous dimensions
that characterize the scaling behavior at the various fixed points of the
renormalization group flow diagram. They appear to be in strong agreement with
those predicted within the nonperturbative context.
