 In this context "strong approximation" is the statement that "S" when reduced generates the full group of points of "G" over the prime fields with "p" elements, when "p" is large enough.It is equivalent to the Cayley graphs being connected (when "p" is large enough), or that the locally constant functions on these graphs are constant, so that the eigenspace for the first eigenvalue is one-dimensional.Superstrong approximation therefore is a concrete quantitative improvement on these statements.