The effect of the inclusion of As antisites in the diluted magnetic semiconductor (Ga, Mn)As is studied within the density functional theory in the local spin density approximation. In the case of the homogeneous distribution of Mn ions, we find that the ferromagnetism is weakened by the presence of the antisites. This is due to the compensation of the free holes which mediate the long-range ferromagnetic order. In contrast, when two Mn ions are coupled through only one As ion, the ferromagnetic and antiferromagnetic states are comparable in energy. In this case, the magnetic ground state depends on: (i) the position of the As antisites relative to the Mn, and (ii) the As antisite concentration. We explain our results using a model of competing antiferromagnetic super exchange and ferromagnetic double exchange via localized Zener carriers. (C) 2001 American Institute of Physics.