  We calculate the system-size-over-wave-length ($M$) dependence of
sample-to-sample conductance fluctuations, using the open kicked rotator to
model chaotic scattering in a ballistic quantum dot coupled by two $N$-mode
point contacts to electron reservoirs. Both a fully quantum mechanical and a
semiclassical calculation are presented, and found to be in good agreement. The
mean squared conductance fluctuations reach the universal quantum limit of
random-matrix-theory for small systems. For large systems they increase
$\propto M^2$ at fixed mean dwell time $\tau_D \propto M/N$. The universal
quantum fluctuations dominate over the nonuniversal classical fluctuations if
$N < \sqrt{M}$. When expressed as a ratio of time scales, the
quantum-to-classical crossover is governed by the ratio of Ehrenfest time and
ergodic time.
