  Several conditions are given when a packing of equal disks in a torus is
locally maximally dense, where the torus is defined as the quotient of the
plane by a two-dimensional lattice. Conjectures are presented that claim that
the density of any strictly jammed packings, whose graph does not consist of
all triangles and the torus lattice is the standard triangular lattice, is at
most $\frac{n}{n+1}\frac{\pi}{\sqrt{12}}$, where $n$ is the number of packing
disks. Several classes of collectively jammed packings are presented where the
conjecture holds.
