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

TL;DR

This paper introduces an algorithm for creating efficient lattice-based template banks for gravitational wave searches, improving coverage of parameter spaces by leveraging optimal lattice coverings, especially in low to moderate dimensions.

Contribution

It presents a new algorithm for generating lattice template banks tailored to constant-coefficient metrics, demonstrating its application in dimensions 2 to 4.

Findings

Efficient lattice template banks can be generated for dimensions 2-4.

The A_n* lattice provides near-optimal coverage in low dimensions.

The method improves search efficiency over hyper-cubic lattices.

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 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.