The sequencers I own allow for quantized 16th note triplet input by selecting 1/24 as the note length. Some of my sequencers also allow for time signatures with 24 as the bottom number. This is similar for 8th note triplets, etc.
However, looking at a list of note values on Wikipedia, there are no 6th, 12th, 24th, or 48th notes, which makes it look like my sequencers are just including those denotations as a convenience (?) for users who aren't theory inclined.
Is the phrase "24th note" ever used in lieu of "16th note triplet"? If so, can there be a time signature with 24 on the bottom?