Ohioan, I think you are referring to the wood along the BOTTOM of the lower fore-end - under the rod hole. In my opinion, this wood is often left much too thick by us who would emulate the longrifle. So I am going out on the limb to say that 1/8" is the maximum, and 1/16" the minimum. Otherwise the stock from the barrel to the trigger guard is way to thick and clunky looking. I've built them that way, and don't like the look at all.
Now, one of the most important considerations, to achieve the slim vertical dimension, is to have the WEB between the barrel and rod hole as thin as you can get away with. I think David is speaking of this web, rather than the bottom of the fore-end. Together with a minimal web and a tapered rod in a 5/16" rod hole, this gives a person the best chance to get the narrow profile.
How do you measure these things? Drill a 1/16" hole through the web in the barrel channel at the breech, into the rod hole. Insert a wire into the hole and measure where it stops on the bottom of the rod hole. Transpose this measurement to the side of the stock opposite this location, and see where the bottom of the rod hole is on the profile of the stock. This will show how much wood remains below in the lower fore-end. You should already have several things drawn on the wood - the bottom of the barrel channel, the web, and the rod hole. Now you can draw the bottom line as well.