The idea of Twisting in MT comes from the discussion with Prof. Nobuo Yoneda who left us in Apr. 1996. The paper is dedicated to his memory.

A previous ancestor of MT, Twisted GFSR is a joint work of Matsumoto and Y. Kurita.

MT is a descent of F2 linear generators and heavily depends on the researches by Professors M. Fushimi, S. Tezuka, P. Lecuyer, R. Couture, H. Niederreiter, and many many other researchers whose names we omit here.

The research of MT is helped by Dept. of Math of Keio University, RIMS at Kyoto University, CRM of Montreal University, Max-Planck-Institute for Mathematics, Salzburg University, and many other institutes, and supported by a Monbusho grant.

MT uses many existing ideas. In particular, we are thankful to the following persons.
N. Yoneda, P. L'Ecuyer, R. Couture, H. Niederreiter, P. Hellekalek, M. Fushimi, S. Tezuka, Y. Kurita, D. Knuth, H. Leeb, S. Wegenkittl, T. Cooper, M. Rieffel, H. Enomoto, and many many persons who gave us valuable comments, including the users of TT800, a previous twisted generator.