Achieving high-quality pseudo-random numbers necessitates sophisticated generator designs, particularly in scientific simulations. This chapter investigates the development and implementation of large-order Multiple Recursive Generators (MRGs), which surpass traditional Linear Congruential Generators in both period length and distribution properties. The limitations of classical approaches, including inadequate dimensional uniformity, highlight the need for MRGs. Various aspects, such as memory requirements and initialization costs, are discussed in relation to large-order MRGs. Additionally, this chapter introduces DX generators as an extension of MRGs, illustrating their empirical advantages and practical deployment strategies.