FCC Rule Part 15.219 allows a 10-foot (3-meter) antenna length for transmission, far shorter than the more than 100-foot length required for a proper resonant match between the transmitter's output and the antenna. To some degree this mismatch can be compensated for by a loading coil, and even more so by designing the transmitter's output for high-impedance rather than the conventional 50-ohms. This is true for vertical antennas, but what about more compact designs occupying smaller spaces?
Loop antennas offer yet unexplored potential for part 15 low power radiation, so I believe. HAM radio hobbyists have had success communicating with loops. This YouTube video takes a look at one experimental effort:
A Home-Built Loop antenna Project
Self correction.
In my opening entry on this subject I flipped the impedance requirements needed to determine the best loading characteristics between a simple 10-foot wire vertical antenna vs. a loading coil and antenna. The original source of this information is found at the SSTran website:
Modifications to AMT3000 Transmitter for base-loaded coil