  We investigate some extremal cases of exactness constant and completely
bounded projection constant. More precisely, for an $n$-dimensional operator
space $E$ we prove that $\lambda_{cb}(E) = \sqrt{n}$ if and only if $ex(E) =
\sqrt{n}$, which is equivalent to $\lambda_{cb}(E) < \sqrt{n}$ if and only if
$ex(E) < \sqrt{n}$.
