Table 1 List of the size of the physical Hilbert space, \(N_{\mathrm{conf}}\), on a ladder of size N for \(D_{3}\) and \(D_{4}\). The configurations are enumerated by a set of integers \(\{j_{i}, i=1,2,\ldots ,3N \}\) characterizing the irrep of each link on whereby Gauss’s law is satisfied at each site