  We consider packings of congruent circles on a square flat torus, i.e.,
periodic (w.r.t. a square lattice) planar circle packings, with the maximal
circle radius. This problem is interesting due to a practical reason - the
problem of "super resolution of images." We have found optimal arrangements for
N=6, 7 and 8 circles. Surprisingly, for the case N=7 there are three different
optimal arrangements. Our proof is based on a computer enumeration of toroidal
irreducible contact graphs.
