81 pitches? That would be impossible unless the the pitcher had a 180 mph fastball and the catcher was a Cyberdyne Systems Model 101 Terminator.
You could have 27 first pitch foul ball outs...
Maybe Greg Maddox against a Little League team. It would have to be someone with immaculate control because in all likelihood he'd have to throw 81 straight strikes. That's hard to do. Plus, he has to have enough velocity and/or movement to keep the hitters from making contact into fair ground (a foul ball would be okay as long as it wasn't done with two strikes).
If a 9-pitch, 3-strikeout inning is an immaculate inning, what would baseball people call 9 of them back-to-back-to-back for a full perfect game? Given that an immaculate inning has only been done about 100 times in the history of major league baseball, the odds of any player doing it 9 straight times is infinitesimally small. Probably like 0.[several hundred zeros] something.