From MSC Big Book page 273:
Example - 1⁄4-20 NC H3
In addition to the nominal size and pitch of a tap, there is another important
dimensional factor to be considered in selecting a ground thread tap. This is
the H limit of the pitch diameter of a tap. H means (high) above basic pitch
diameter(A "D" corresponds to metric threads). These tap limits have been
established to provide a choice in the selection of the tap size best suited to
produce the class of thread desired. The difference in size from one H limit to
the next is 0.0005 increments for taps through 1" diameter. Sizes over 1"
diameter are separated by .001 diameter increments. If the threads in the part
are too loose, smaller numbers such as H1 or H2 are used. If the threads are
too tight, the H limit number is increased. Proper selection of the H limit
number ensures that the threads are within the tolerance required by the part
print. Best rule of thumb: always select the largest “H” limit possible to achieve.
Tom