Geometric time delay interferometry up to 30-link: Efficient algorithm and combination library

Time delay interferometry (TDI) serves as a crucial data preprocessing technique in space-based gravitational wave detection, primarily employed for suppressing laser noises. Geometric TDI recasts the design of TDI combinations as the construction of a virtual synthesized interferometer, thereby offering an intuitive spacetime diagram that complements traditional algebraic approaches. This work focuses on geometric TDI, presenting a high-efficiency search algorithm and establishing the most comprehensive geometric TDI combination library to date. Through a four-stage algorithmic framework comprising virtual optical path construction, laser noise residual evaluation, combination filtering with path pairing, and duplicate combination removal, we accelerate the search by more than three orders of magnitude. This advancement has enabled, for the first time, the complete enumeration of geometric TDI combinations up to 30-link. The resulting open-source library contains millions of categorized modified first-generation, second-generation, and modified second-generation TDI combinations, providing an unprecedented resource for forthcoming space-based gravitational wave detection missions.