  A lattice is called periodic extreme if it cannot locally be modified to
yield a better periodic sphere packing. It is called strict periodic extreme if
its sphere packing density is an isolated local optimum among periodic point
sets. In this note we show that a lattice is periodic extreme if and only if it
is extreme, that is, locally optimal among lattices. Moreover, we show that a
lattice is strict periodic extreme if and only if it is extreme and
non-floating.
