Ti/Al/Ni/Au ohmic contacts were formed on heavily doped n+ metal-polar GaN samples with various Si doping concentrations grown by molecular beam epitaxy. The contact resistivity (RC) and sheet resistance (Rsh) as a function of corresponding GaN free carrier concentration (n) were measured. Very low RC values (<0.09 Ω mm) were obtained, with a minimum RC of 0.035 Ω mm on a sample with a room temperature carrier concentration of ∼5 × 1019 cm−3. Based on the systematic study, the role of RC and Rsh is discussed in the context of regrown n+ GaN ohmic contacts for GaN based high electron mobility transistors.