  A method is presented for the calculation of all exact ground states of
diluted antiferromagnets and random field systems in an arbitrary range of
fields. It works by calculating all jump-fields B,\Delta where the system
changes it's ground state. For each field value all degenerated ground states
are represented by a set of (anti-) ferromagnetic clusters and a relation
between the clusters. So a complete description of the ground state structure
of these systems is possible.
  Systems are investigated up to size 48^3 on the whole field-range and up to
160^3 for some particular fields. The behavior of order parameters is
investigated, the number of jumps is analyzed and the degree of degeneracy as
functions of size and fields is calculated.
