  One of the most striking draw-backs of standard lattice gas methods over
lattice Boltzmann methods is a much more limited range of transport parameters
that can be achieved. It is common for lattice Boltzmann methods to use
over-relaxation to achieve arbitrarily small transport parameters in the
hydrodynamic equations. Here, we show that it is possible to implement
over-relaxation for integer lattice gases. For simplicity we focus here on
lattice gases for the diffusion equation. We demonstrate that adding a flipping
operation to lattice gases results in a multi-relaxation time lattice Boltzmann
scheme with over-relaxation in the Boltzmann limit.
