We simulate late-stage coarsening of a 3D symmetric binary fluid using a lattice Boltzmann method. With reduced lengths and times, l and t, respectively (with scales set by viscosity, density, and surface tension), our data sets cover 1 less than or similar to l less than or similar to 10(5) and 10 less than or similar to t less than or similar to 10(8). We achieve Reynolds numbers approaching 350. At Re greater than or similar to 100 we find clear evidence of Furukawa's inertial scaling (l similar to t(2/3)), although the crossover from the viscous regime (l similar to t) is very broad. Though it cannot be ruled out, we find no indication that Re is self-limiting (l similar to t(1/2)) as proposed by M. Grant and K.R. Elder [Phys. Rev. Lett. S2, 14 (1999)].