SkiBum326:
Correct me if I'm wrong,
Oh, he will!
In short, you must assume the design is already optimised to obtain the best performance from the parts available and that no "simple" modification will drastically enhance its performance.
A larger coil will increase range, but you then have to work out how to design it so that it tunes to the frequency. Not trivial.
I think we have forgotten about the transformer by now. 