We want to study the BPS spectra of a special class of supersymmetric quantum field theories (SUSY QFTs) relevant for computations in M-Theory and Open Topological String Theory. We do this by constructing Exponential Networks on the moduli space of Fayet–Iliopoulos coupling in our SUSY QFT. Constructing this in detail will help us make important statements about the general nature of the corresponding BPS spectra, and this is why we need to use these computation resources.