While being of persistent interest for the integration of lattice-matched laser devices with silicon circuits, the electronic structure of dilute nitride III/V-semiconductors has presented a challenge to ab initio computational approaches. The origin of the computational problems is the strong distortion exerted by the N atoms on most host materials. Here, these issues are resolved by combining density functional theory calculations based on the meta-GGA functional presented by Tran and Blaha (TB09) with a supercell approach for the dilute nitride Ga(NAs). Exploring the requirements posed to supercells, it is shown that the distortion field of a single N atom must be allowed to decrease so far that it does not overlap with its periodic images. This also prevents spurious electronic interactions between translational symmetric atoms, allowing us to compute band gaps in very good agreement with experimentally derived reference values. In addition to existing approaches, these results offer a promising ab initio avenue to the electronic structure of dilute nitride semiconductor compounds.