A high-gain digitally tuned antenna system comprises a modified swept-back fractal (MSBF) radiator element, with the fractal preferably being a Sierpinski carpet fractal based on a parallelogram. A digital tuning circuit coupled to the radiator comprises an array of inductors which can be selectively connected to form a network which tunes the antenna system to a selected tuning frequency. The system is preferably arranged to selectively connect the inductors in series such that the combined inductances substantially cancel the capacitance of the radiator at a selected tuning frequency. The antenna system is preferably arranged to operate over the 30-88 MHz, 108-174 MHz, and 225-600 MHz bands, with a radiator height of 15″ or less.