  Improving the frequency precision by synchronizing a lattice of oscillators
is studied in the phase reduction limit. For the most commonly studied case of
purely dissipative phase coupling (the Kuramoto model) I confirm that the
frequency precision of N oscillators perturbed by independent noise sources is
improved by a factor N as expected from simple averaging arguments. In the
presence of reactive coupling, such as will typically be the case for
non-dissipatively coupled oscillators based on high-Q resonators, the
synchronized state consists of target like waves radiating from a local source
which is a region of higher frequency oscillators. In this state all the
oscillators evolve with the same frequency, however I show that the improvement
of the frequency precision is independent of N for large N, but instead depends
on the disorder and reflects the dependence of the frequency of the
synchronized state on just those oscillators in the source region of the waves.
