The use of voxelized sources (i.e. from PET or SPECT images of patients) is widespread in Monte Carlo (MC) simulations for medical applications. Hence, spatial source sampling is the first step of the simulation and consists in sampling the position of particles to be simulated according to a given 3D voxelized activity map. This is usually done by calculating the Cumulative Distribution Function (CDF) in each dimension, reducing the N points sampling according to the activity distribution over the domain Ω ⊂ ℝd (d=2,3) to a N points sampling according to a uniform distribution over [0, 1]d. This method, known as the Inverse Transform Sampling (ITS), requires N uniformly sampled points in [0,1]d then mapped to Ω in order to simulate N primary particles from the source. In classical MC simulations, these N points are uniformly sampled pseudo-randomly and independently, leading to worst-case scenarios where they are poorly equidistributed. We propose here to investigate quasi-random sequences, whose usage in Computer Graphics is very effective and is still being improved [1], in order to increase the sampling efficiency. The method can also be used with geometrical importance sampling (GIS).