  The limits of the areal storage density as can be achieved with heat assisted
magnetic recording (HAMR) are still an open issue. We want to address this
central question and present the design of a possible bit patterned medium with
an areal storage density above 10 Tb/in$^2$. The model uses hard magnetic
recording grains with 5 nm diameter and 10 nm height. It assumes a realistic
distribution of the Curie temperature of the underlying material as well as a
realistic distribution of the grain size and the grain position. In order to
compute the areal density we analyze the detailed switching behavior of a
recording bit under different external conditions, which allows to compute the
bit error rate of a recording process (shingled and conventional) for different
grain spacings and write head positions. Hence, we are able to optimize the
areal density of the presented medium.
