Transport properties of finite antidots arrays, with large lattice parameters and electron densities, may be roughly understood from a semiclassical approach. For weak magnetic fields, commensurability effects between the antidot spacing and the cyclotron radius are present with interference patterns superimposed on the magnetoresistivity. For higher magnetic fields, transport through edge states becomes relevant. In the present work, we discuss a completely different behavior that should occur in the quantum limit, for short lattice parameters and small electron densities. The key feature is the formation of surface Tamm-like states within the gap of the lowest bulk bands of a finite antidot lattice. The surface of a finite antidot superlattice may act as an isolated quantum ring, a coupler of the superlattice to the contacts, or a barrier between the bulk of the antidot lattice and the contacts, as a function solely of the applied magnetic field. © 2001 The American Physical Society.