  The quasi-random discrete ordinates method (QRDOM) is here proposed for the
approximation of transport problems. Its central idea is to explore a quasi
Monte Carlo integration within the classical source iteration technique. It
preserves the main characteristics of the discrete ordinates method, but it has
the advantage of providing mitigated ray effect solutions. The QRDOM is
discussed in details for applications to one-group transport problems with
isotropic scattering in rectangular domains. The method is tested against
benchmark problems for which DOM solutions are known to suffer from the ray
effects. The numerical experiments indicate that the QRDOM provides accurate
results and it demands less discrete ordinates per source iteration when
compared against the classical DOM.
