Illumination simulation involving participating media is computationally intensive. The overall aspect of the material depends on simulating a large number of scattering events inside the material. Combined, the contributions of these scattering events are a smooth illumination. Computing them using ray-tracing or photon-mapping algorithms is expensive: convergence time is high, and pictures before convergence are low quality. In this paper, we precompute the result of multiple scattering events, assuming an infinite medium, and store it in two 4D tables. These precomputed tables can be used with many rendering algorithms, such as Virtual Ray Lights (VRL), Unified Point Beams and Paths (UPBP) or Manifold Exploration Metropolis Light Transport (MEMLT), greatly reducing the convergence time. The original algorithm takes care of low order scattering (single and double scattering), while our precomputations are used for multiple scattering (more than two scattering events).