There are time signatures in 16's.
In all reality, it can all be broken down into 4's though....

15/16 = one measure of 8/8 and one measure of 7/8
8/8 = 4/4 and 4/4
7/8 = 4/4 and 3/4

So, 15/16 can be thought as 3 measures of 4/4 and one measure of 3/4 in any order, depending on the type of notes played (quarter, eighth, etc....)

Please correct me if I'm wrong, I'm by no means an expert on time signatures, I just play......this is how our drummer explained it to me..