To go a little further, there isn't an actual "H-0" limit, but people use it to mean a "dead on size tap, nothing added" .
However, nothing like that actually exists. It's either H1 where the tap can be between on size and + 1/2 thousandth" over , or L1 where the tap is somewhere between on size & a 1/2 thousandth" under.
Some taps and gauges are very expensive due to the measuring required, for both the manufacturing and certification. Seldom this precision is actually required. We used to make some parts that used a left hand and a right hand thread. When assembled the requirement was that it had less than 18 deg of rotation of the nut in backlash. Due to the pitch, the most total clearance between the inner insert, the outer thread etc was 0.0007 inches of linear play. We often made them with 0.0004 linear play. We never used taps or dies, but I chose to screwcut all the threads. Made go nogo gauges for all the threads. Knowing the tolerance of the taps or threads is always good to know though. You can rework an oversized tap to a smaller pitch diameter, but you can't make a small bigger. Generally taps are close to the upper limit, and dies are closer to the lower limit. One thing that can be over looked is the accuracy of the pitch for the tap or die as well. For most things, that does not become a issue however.