  The existence of a strongly coupled ultraviolet fixed point in 4-dimensional
lattice models as they cross into the conformal window has long been
hypothesized. The SU(3) gauge system with 8 fundamental fermions is a good
candidate to study this phenomenon as it is expected to be very close to the
opening of the conformal window. I study the system using staggered lattice
fermions in the chiral limit. My numerical simulations employ improved lattice
actions that include heavy Pauli-Villars (PV) type bosons. This modification
does not affect the infrared dynamics but greatly reduces the ultraviolet
fluctuations, thus allowing the study of stronger renormalized couplings than
previously possible. I consider two different PV actions and find that both
show an apparent continuous phase transition in the 8-flavor system.
  I investigate the critical behavior using finite size scaling of the
renormalized gradient flow coupling. The finite size scaling curve-collapse
analysis predicts a first order phase transition consistent with discontinuity
exponent $\nu=1/4$ in the system without PV bosons. The scaling analysis with
the PV boson actions is not consistent with a first order phase transition. The
numerical data are well described by "walking scaling" corresponding to a
renormalization group $\beta$ function that just touches zero, $\beta(g^2) \sim
(g^2 - g^2_\star)^2$, though second order scaling cannot be excluded. Walking
scaling could imply that the 8-flavor system is the opening of the conformal
window, an exciting possibility that could be related to t'Hooft anomaly
cancellation of the system.
