  The dependence of $K^+$ production on the nuclear equation of state is
investigated in heavy ion collisions. An increase of the excitation function of
$K^+$ multiplicities obtained in heavy ($Au+Au$) over light ($C+C$) systems
when going far below threshold which has been observed by the KaoS
Collaboration strongly favours a soft equation of state. This observation holds
despite of the influence of an in-medium kaon potential predicted by effective
chiral models which is necessary to reproduce the experimental $K^+$ yields.
