  We present an open version of the symplectic kicked rotator as a stroboscopic
model of electrical conduction through an open ballistic quantum dot with
spin-orbit scattering. We demonstrate numerically and analytically that the
model reproduces the universal weak localization and weak anti-localization
peak in the magnetoconductance, as predicted by random-matrix theory (RMT). We
also study the transition from weak localization to weak anti-localization with
increasing strength of the spin-orbit scattering, and find agreement with RMT.
