本文探討二階與三階遞迴亂數產生器之一些特性，同時提出一些啟發式方法，可以有效的搜尋具有良好格子架構的多階遞迴亂數產生器。亂數的齊一性與獨立性採稀疏佔有性檢定，所有跡象均顯示二階與三階遞迴亂數產生器優於傳統所使用的質數乘餘產生器，而三階產生器略優於二階產生器。本文同時推薦一些亂數產生器，特別適用於大規模之模擬研究。

　　　　　This paper discusses some important properties of the second order and third order multiple recursive random number (RN) generators. A partial exhaustive search method which is able to effectively find the multiple recursive generators (MRGs) with satisfactory lattice structure for the RNs produced is proposed. Uniformity and independence are examined by the stringent sparse-occupancy tests. Every evidence indicates that the second order and third order MRGs clearly override the traditional prime modulus multiplicative congruential generator in an average sense, and the third order MRG is marginally superior to the second order MRG. Several MRGs suggested in this aper are well suited for large-scale simulation studies.