  This is the second paper in a series describing a numerical implementation of
the conformal Einstein equation. This paper deals with the technical details of
the numerical code used to perform numerical time evolutions from a "minimal"
set of data.
  We outline the numerical construction of a complete set of data for our
equations from a minimal set of data. The second and the fourth order
discretisations, which are used for the construction of the complete data set
and for the numerical integration of the time evolution equations, are
described and their efficiencies are compared. By using the fourth order scheme
we reduce our computer resource requirements --- with respect to memory as well
as computation time --- by at least two orders of magnitude as compared to the
second order scheme.
