I checked the GIBRALTARS and the ROC's out, their short base bottoms are 16" to the spindle at zero, add your seat top and your in the 20's as the spec's note:
Short Throne Base
Adjusts from 16" to 24" in height
Seat fits onto a 7/8" diameter shaft
Adjusts from 20" to 28" in height
B9608S Short throne base
16" isn't really low IMO. I have STADIUM throne bases that go down to 12.5" without the tops, tho they're 1" tubes, not spindles.
ROC and GIBRALTAR need to get a short base together, there's a strong kids market and quite a few adults would prefer and could make a smaller, shorter, lighter base work.
Im willing to bet 95% of the drummers out there do not
have their spindles/seat posts above 24"