  Symmetry-induced vortex-antivortex configurations in superconducting squares
and triangles were predicted earlier; yet, they have not been resolved in
experiment up to date. Namely, with vortex-antivortex states being highly
unstable with respect to defects and temperature fluctuations, it is very
unlikely that samples can be fabricated with the needed quality. Here we show
how these drawbacks can be overcome by strategically placed nanoholes in the
sample. As a result, (i) the actual shape of the sample becomes far less
important, (ii) the stability of the vortex-antivortex configurations in
general is substantially enhanced, and (iii) states comprising novel
giant-antivortices (with higher winding numbers) become energetically favorable
in perforated disks. In the analysis, we stress the potent of strong screening
to destabilize the vortex-antivortex states. In turn, the screening-symmetry
competition favors stabilization of new asymmetric ground states, which arise
for small values of the effective Ginzburg-Landau parameter kappa.
