The diffusion constant and the Lyapunov exponent for the spatially periodic
Lorentz gas are evaluated numerically in terms of periodic orbits. A symbolic
description of the dynamics reduced to a fundamental domain is used to generate
the shortes periodic orbits. Applied to a dilute gas with finite horizon, the
theory works well, but for the dense Lorentz gas the convergence is hampered by
the strong pruning of the admissable orbits.