Reconstruction Plans and Efficient Rank-1 Lattice Construction for Chebyshev Expansions Over Lower Sets

This study focuses on constructing efficient rank-1 lattices that enable the exact integration and reconstruction of functions within Chebyshev spaces, based on finite lower index sets. We establish the equivalence of different reconstruction plans under specific conditions for certain lower sets. Furthermore, we introduce a heuristic component-by-component (CBC) algorithm that efficiently identifies admissible generating vectors and suitable numbers of nodes $n$, optimizing both memory usage and computational time.