  We numerically examine the large-q asymptotics of the q-state random bond
Potts model. Special attention is paid to the parametrisation of the critical
line, which is determined by combining the loop representation of the transfer
matrix with Zamolodchikov's c-theorem. Asymptotically the central charge seems
to behave like c(q) = 1/2 log_2(q) + O(1). Very accurate values of the bulk
magnetic exponent x_1 are then extracted by performing Monte Carlo simulations
directly at the critical point. As q -> infinity, these seem to tend to a
non-trivial limit, x_1 -> 0.192 +- 0.002.
