  Recent work suggested that the traditional picture of the corona above the
quiet Sun being rooted in the magnetic concentrations of the chromospheric
network alone is strongly questionable. Building on that previous study we
explore the impact of magnetic configurations in the photosphere and the low
corona on the magnetic connectivity from the network to the corona.
Observational studies of this connectivity are often utilizing magnetic field
extrapolations. However, it is open to which extent such extrapolations really
represent the connectivity found on the Sun, as observations are not able to
resolve all fine scale magnetic structures. The present numerical experiments
aim at contributing to this question. We investigated random
salt-and-pepper-type distributions of kilo-Gauss internetwork flux elements
carrying some $10^{15}$ to $10^{17}$ Mx, which are hardly distinguishable by
current observational techniques. These photospheric distributions are then
extrapolated into the corona using different sets of boundary conditions at the
bottom and the top. This allows us to investigate the fraction of network flux
which is connected to the corona, as well as the locations of those coronal
regions which are connected to the network patches. We find that with current
instrumentation one cannot really determine from observations, which regions on
the quiet Sun surface, i.e. in the network and internetwork, are connected to
which parts of the corona through extrapolation techniques. Future
spectro-polarimetric instruments, such as with Solar B or GREGOR, will provide
a higher sensitivity, and studies like the present one could help to estimate
to which extent one can then pinpoint the connection from the chromosphere to
the corona.
