A scalable design method to perform multilevel network minimization targeting k-input look-up-tables (k-LUT) is proposed. It contributes toward the big size logic design theory and application. The method is based on the resubstitution which is formulated and solved as a covering task: A node function, which depends on an input selected for the resubstitution, is split into a set of dichotomies. The selected input is removed, and the minimal set of inputs to cover the dichotomies are sought. The resubstitution procedure runs on top of the k-LUT network produced by existing synthesis tools (SIS, ABC). Scalability is achieved by the extraction of windows, which satisfy given constraints (number of inputs, nodes, etc.). The window logic is described using the proposed extended programmable logic array (PLA) table, which contains information about don't cares. Experiments show that the best networks obtained using SIS and ABC can be further improved by applying our method. Also, big benchmarks from the EPFL library are processed, and for almost half of them, improvements are achieved.