I've always more or less assumed that the number is related to the order in which they were shattered in, but something in my gut tells me that Brandon would attach a more complex meaning to the number than that. I feel as if we are on the right track but missing important information.
If someone could get a WoB on if there are any shards associated with a number that is not 1 through 16 then it help confirm this line of thought, or point us to the right one if we are wrong.