The skill to produce satisfactory sequences of random numbers is one of the crucial tasks of cryptography. For this reason a lot of types of random number generators in the literature are described. Many of known and generally used random number generators are not excellent enough for modern cryptographic applications, so it's worth trying to develop new generators. It has been experimentally shown that there exist a lot of QFFSR sequences generators of diverse structure, many of them giving sequences of QF(q) elements with a good randomness. Therefore, the hard problem of optimizing QFFSR sequences generators has been indicated.