We demonstrate a reliable fabrication method to produce plasmonic dipole nanoantennas with gap values in the range of 3.5-20 nm. The method combines electron beam lithography to create gold nanorods and helium focused ion beam milling to cut the gaps. Results show a reproducibility within 1 nm. Scattering spectra of antennas show a red shift of resonance wavelengths and an increase of the intensity of resonance peaks with a decrease of the gap size, which is in agreement with finite element simulations. The measured refractive index sensitivity was about 250 nm per refractive index unit for antennas with gap values below 5 nm.