Mg-doped GaN with a net acceptor concentration (NA-ND) in the high 10 19 cm(-3) range was grown using ammonia molecular-beam epitaxy. Electrical properties of NiO contact on this heavily doped p-type GaN were investigated. A potential-barrier height of 0.24 eV was extracted from the relationship between N-A-N-D and the specific contact resistivity (rho c). We found that there is an optimum N-A-N-D value of 5 x 10(19) cm(-3) for which rho c is as low as 2 x 10(-5) Omega cm(2). This low rho c is ascribed to hole tunneling through the potential barrier at the NiO/p(+)-GaN interface, which is well accounted for by the field-emission model. Published by AIP Publishing.