The efficient implementation of the spectral test is crucial for analyzing the lattice structure of multiplicative recursive generators (MRGs). This chapter first reviews conventional spectral test techniques, focusing on the construction of basis matrices via companion matrices. A detailed mathematical framework is presented to illustrate how sequentially generated values fit within a lattice structure. Building upon this foundation, a novel optimization method is proposed, significantly improving computational efficiency. The discussion integrates both theoretical insights and practical techniques, enhancing the feasibility of large-scale spectral testing.