  The recent work of \cite{CRT,DonohoPol} rigorously proved (in a large
dimensional and statistical context) that if the number of equations
(measurements in the compressed sensing terminology) in the system is
proportional to the length of the unknown vector then there is a sparsity
(number of non-zero elements of the unknown vector) also proportional to the
length of the unknown vector such that $\ell_1$-optimization algorithm succeeds
in solving the system. In more recent papers
\cite{StojnicCSetamBlock09,StojnicICASSP09block,StojnicJSTSP09} we considered
under-determined systems with the so-called \textbf{block}-sparse solutions. In
a large dimensional and statistical context in \cite{StojnicCSetamBlock09} we
determined lower bounds on the values of allowable sparsity for any given
number (proportional to the length of the unknown vector) of equations such
that an $\ell_2/\ell_1$-optimization algorithm succeeds in solving the system.
These lower bounds happened to be in a solid numerical agreement with what one
can observe through numerical experiments. Here we derive the corresponding
upper bounds. Moreover, the upper bounds that we obtain in this paper match the
lower bounds from \cite{StojnicCSetamBlock09} and ultimately make them optimal.
