  This paper continues arXiv.org:math.AG/0609256, arXiv:0708.3991 and
arXiv:0710.0162 .
  Using authors's methods of 1980, 1981, some explicit finite sets of number
fields containing all ground fields of arithmetic hyperbolic reflection groups
in dimension at least 3 are defined, and explicit bounds of their degrees (over
Q) are obtained.
  Thus, now, explicit bound of degree of ground fields of arithmetic hyperbolic
reflection groups is known in all dimensions. Thus, now, we can, in principle,
obtain effective finite classification of arithmetic hyperbolic reflection
groups in all dimensions together.
