  Using the Landauer formula and a random matrix model, we investigate the
autocorrelation function of the conductance versus magnetic field strength for
ballistic electron transport through few-channel microstructures with the shape
of a classically chaotic billiard coupled to ideal leads. This function depends
on the total number M of channels and the parameter t which measures the
difference in magnetic field strengths. Using the supersymmetry technique, we
calculate for any value of M the leading terms of the asymptotic expansion for
small t. We pay particular attention to the evaluation of the boundary terms.
For small values of M, we supplement this analytical study by a numerical
simulation. We compare our results with the squared Lorentzian suggested by
semiclassical theory and valid for large M. For small M, we present evidence
for non--analytic behavior of the autocorrelation function at t = 0.
