Search for gravitational waves: lattice covering of flat parameter spaces

We derive a simple algebraic criterion to select the optimal detector network for a coherent wide parameter-space (all-sky) search for continuous gravitational waves. Optimality in this context is defined as providing the highest (average) sensitivity per computing cost. This criterion is a direct consequence of the properties of the multi-detector F-statistic metric, which has been derived recently. Interestingly, the choice of the optimal network only depends on the noise-levels and duty-cycles of the respective detectors, and not on the available computing power