  Four-dimensional (4D) simplicial quantum gravity coupled to both scalar
fields (N_X) and gauge fields (N_A) has been studied using Monte-Carlo
simulations. The matter dependence of the string susceptibility exponent
gamma^{(4)} is estimated. Furthermore, we compare our numerical results with
Background-Metric-Independent (BMI) formulation conjectured to describe the
quantum field theory of gravity in 4D. The numerical results suggest that the
4D simplicial quantum gravity is related to the conformal gravity in 4D.
Therefore, we propose a phase structure in detail with adding both scalar and
gauge fields and discuss the possibility and the property of a continuum theory
of 4D Euclidean simplicial quantum gravity.
