  Cooperative scattering in cold atoms has gained renewed interest, in
particular in the context of single-photon superradiance, with the recent
experimental observation of super-and subradiance in dilute atomic clouds.
Numerical simulations to support experimental signatures of cooperative
scattering are often limited by the number of dipoles which can be treated,
well below the number of atoms in the experiments. In this paper, we provide
systematic numerical studies aimed at matching the regime of dilute atomic
clouds. We use a scalar coupled-dipole model in the low excitation limit and an
exclusion volume to avoid density-related effects. Scaling laws for super-and
subradiance are obtained and the limits of numerical studies are pointed out.
We also illustrate the cooperative nature of light scattering by considering an
incident laser field, where half of the beam has a $\pi$ phase shift. The
enhanced subradiance obtained under such condition provides an additional
signature of the role of coherence in the detected signal.
