  We study the three-dimensional gauge glass model in the limit of strong
screening by using a minimum cost flow algorithm, enabling us to obtain EXACT
ground states for systems of linear size L<=48. By calculating the domain-wall
energy, we obtain the stiffness exponent theta = -0.95+/-0.03, indicating the
absence of a finite temperature phase transition, and the thermal exponent
nu=1.05+/-0.03. We discuss the sensitivity of the ground state with respect to
small perturbations of the disorder and determine the overlap length, which is
characterized by the chaos exponent zeta=3.9+/-0.2, implying strong chaos.
