The asymptotically background-free quantum gravity is a renormalizable quantum field theory formulated in a hybrid manner that combines conformal field theory, a typical nonperturbative method, and perturbation theory. As an approach to formulate this theory in a completely nonperturbative manner, a method based on dynamical triangulationsDynamical triangulation has been proposed. This is a method of considering Euclidean spacetime as in lattice gauge theory and dividing it into random lattices for examination.