Wiring size for 100amp sub panel
I would say 1/0 aluminum from the wire size calculator. Any smaller than that and you'll have significant voltage drop. 

You'll need 4 wires - two hots, 1 neutral and 1 ground.  

There are two ways to go.  


Lay a conduit, and have individual wires going through the conduit.  Expensive initial construction, but you can obtain 1/0 wires as individual THWN wires at 50 cents a foot (x4 = $2.00/foot). This also allows adding other stuff such as a switched lighting circuit. You can't put data in a power conduit, though. Depending on the type of conduit, conduit can be the ground, which eliminates one wire. 
use multi-conductor cable.  This is a pre-made cable that has all 4 wires wrapped in a single outer sheath.  (this bundle will be rather stiff.)  Trouble is, multi-conductor cables are not made in every size (or not kept in stock by distributors).  What's more, you must use a type of cable (SER, UF, USE etc.) that is correct for your installation route.  This limits your selection further, and you could wind up having to go as big as 4/0 ($4/foot). 


I often have to go with a larger cable than the calculator said, because my distributor simply doesn't stock my correct size.  This is only a problem with multi-conductor cable; single conductor THWN is generally available in every size if you're working in conduit.