Template-based searches for gravitational waves: efficient lattice covering of flat parameter spaces

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 A(n)* 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 A(n)* template banks in n = 2, 3, 4 dimensions.