Paul,
Lou has given you good advice, Custom Design will do what you ask. I will attempt to briefly answer WHY you can't get what you want from the screening design platform.
Classic screening designs are orthogonal. That means that even the blocks need to be orthogonal, too. There is no way to divide 16 evenly by 3, so you cannot get an orthogonal block. Remember that at this point in the design creation, JMP does not know that you are going to replicate the design 3 times. That is why all of the block sizes are powers of 2 -- that will keep the design orthogonal.
There are ways to "trick" the screening design platform into giving you what you want, but as Lou said, Custom Design will do that without any tricks.
Dan Obermiller