Optimal 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, with computational cost that is proportional to number these points. If fixed, question arises, where should be placed space? The current literature advocates selecting (called ``template bank'') whose Wigner--Seitz (also called Vorono\"{\i}) cells have smallest covering radius ($\ensuremath{\equiv}$ maximal mismatch). Mathematically, such template bank said ``minimum thickness''. Here, realistic populations we compute fraction potential detections which ``lost'' because discrete. We show fixed cost, minimum thickness does not maximize expected detections. Instead, most obtained minimizes particular functional mismatch. For closely spaced templates, lost scale-invariant ``quantizer constant'' $G$, measures average squared distance from nearest template, i.e., This provides straightforward way characterize and compare effectiveness different banks. $G$ mathematically ``optimal quantizer'', maximizes review optimal quantizer banks built as $n$-dimensional lattices, showing even best offer only marginal advantage over based on humble cubic lattice.