  $n$-scales are a generalization of time-scales that has been put forward to
unify continuous and discrete analyses in higher dimensions. In this paper we
investigate massive scalar field theory on a regular $n$-Scale. We have given
the modified field equation that is appropriate to this space-time structure
and gave the mode solutions. If the space-time is discrete we have found that
no massive scalar field can exist. Hence, we concluded that unbounded discrete
space-time cannot exist. If discrete space-time exists, it has to be bounded in
each dimension.
