  We present an example of a complete and minimal Gabor system consisting of
time-frequency shifts of a Gaussian, localized at the coordinate axes in the
time-frequency plane (phase space). Asymptotically, the number of
time-frequency shifts contained in a disk centered at the origin is only 2/pi
times the number of points from the von Neumann lattice found in the same disk.
Requiring a certain regular distribution in phase space, we show that our
system has minimal density among all complete and minimal systems of
time-frequency shifts of a Gaussian.
