This monograph proves that any finite random number sequence is represented by the multiplicative congruential (MC) way. It also shows that an MC random number generator (d, z) formed by the modulus d and the multiplier z should be selected by new regular simplex criteria to give random numbers an excellent disguise of independence.

Naoya Nakazawa and Hiroshi Nakazawa

1. Basic Concepts and Tools 2. Group Structures 3. Designs of MC Generators 4. Lattice Structures 5. Regular Simplexes and Regular Lattices 6. Extended Second-Degree Tests 7. MC Generators with Excellent Statistics 8. MC Random Numbers on Spatial Lattices 9. Random Vector Fields and Random Walks 10. Two Addenda and Closing Comments