We booted the sidewall of a Firestone Radial 18.4 x 38 after running over a shed antler that gashed a ragged hole better than 1 1/2 inches long.  Tried it with a tube, but that didn't last long since the sidewall flexing tore the tube to shreds and then just went back to tubeless.  That was in '03, have had zero problems since. 

btw, this is on a 7610 JD.