  In the presence of both spin-orbit scattering and a magnetic field the
conductance of a chaotic GaAs quantum dot displays quite a rich behavior. Using
a Hamiltonian derived by Aleiner and Falko [Phys. Rev. Lett. 87, 256801 (2001)]
we calculate the weak localization correction and the covariance of the
conductance, as a function of parallel and perpendicular magnetic field and
spin-orbit coupling strength. We also show how the combination of an in-plane
magnetic field and spin-orbit scattering gives rise to a component to the
magnetoconductance that is anti-symmetric with respect to reversal of the
perpendicular component of the magnetic field and how spin-orbit scattering
leads to a "magnetic-field echo" in the conductance autocorrelation function.
Our results can be used for a measurement of the Dresselhaus and Bychkov-Rashba
spin-orbit scattering lengths in a GaAs/GaAlAs heterostructure.
