OP: There is no minimum, it is the maximum current. For example, you have a 5V source and 4 LED's at 1A with a Vf of 4V, which is 12V. The shark must take the 5V and draw enough current to output 1A at 16V, which would be 3.84A at 5V assuming 20% driver inefficiency*. IIRC, 4A is the absolute maximum that the shark can handle (so in other words, this setup would work, but barely), Wayne, can you confirm or deny this?
And yes, I made up 20% inefficiency as a worst case, I'm not sure of the real numbers.
*If you're running it this hard, you're dropping about 4W in heat, so you need your heatsinking sorted!