  The main purpose of this paper is to strengthen our understanding of sofic
mean dimension of two typical classes of sofic group actions. First, we study
finite group actions. We prove that sofic mean dimension of any amenable group
action does not depend on the choice of sofic approximation sequences.
Previously, this result was known only if the acting group is an infinite
amenable group. Moreover, we investigate the full shifts, for all sofic groups
and all alphabets. We show that sofic mean dimension of any full shift depends
purely on its alphabet. Our method is a refinement of the classical technique
in relation to the estimates from above and below, respectively, for mean
dimension of some typical actions. The key point of our results is that they
apply to all compact metrizable spaces without any restriction (in particular,
the alphabet concerned in a full shift and the space involved in a finite group
action are not required to be finite-dimensional).
  Furthermore, we improve the quantitative knowledge of sofic mean dimension,
restricted to finite-dimensional compact metrizable spaces, for those two
typical classes of sofic group actions. As a direct consequence of the main
ingredient of our proof, we obtain the exact value of sofic mean dimension of
all the actions of finite groups on finite-dimensional compact metrizable
spaces. Previously, only an upper bound for these actions was given. Besides,
we also get the exact value of sofic mean dimension of full shifts when the
alphabet is finite-dimensional.
