Template-based searches for gravitational waves: efficient lattice covering of flat parameter spaces
Abstract
The construction of optimal template banks for matched-filtering searches is an example of the sphere covering problem. For parameter spaces with constant-coefficient metrics a (near-) optimal template bank is achieved by the An* lattice, which is the best lattice-covering in dimensions n <= 5, and is close to the best covering known for dimensions n <= 16. Generally this provides a substantially more efficient covering than the simpler hyper-cubic lattice. We present an algorithm for generating lattice template banks for constant-coefficient metrics and we illustrate its implementation by generating An* template banks in n=2,3,4 dimensions.
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