Performance of random template banks

When searching for new gravitational-wave or electromagnetic sources, the $n$ signal parameters (masses, sky location, frequencies,...) are unknown. In practice, one hunts signals at a discrete set of points in parameter space, called template bank. These may be constructed systematically as lattice, alternatively, by placing templates randomly selected space. Here, we calculate fraction lost an $n$-dimensional random bank (compared to very finely spaced bank). This is compared corresponding loss best possible lattice-based banks containing same number grid points. For dimensions $n<4$ significantly outperform ones. However, remarkably, $n>8$, difference negligible. high dimensions, known lattices.