  A Gray code for a combinatorial class is a method for listing the objects in
the class so that successive objects differ in some prespecified, small way,
typically expressed as a bounded Hamming distance. In a previous work, the
authors of the present paper showed, among other things, that the $m$-ary
Reflected Gray Code Order yields a Gray code for the set of restricted growth
functions. Here we further investigate variations of this order relation, and
give the first Gray codes and efficient generating algorithms for bounded
restricted growth functions.
