  It has been shown that finding generic Bell states diagonal entanglement
witnesses (BDEW) for $d_{1}\otimes d_{2}\otimes ....\otimes d_{n}$ systems
exactly reduces to a linear programming if the feasible region be a polygon by
itself and approximately obtains via linear programming if the feasible region
is not a polygon. Since solving linear programming for generic case is
difficult, the multi-qubits, $2\otimes N$ and $3 \otimes 3$ systems for the
special case of generic BDEW for some particular choice of their parameters
have been considered. In the rest of this paper we obtain the optimal non
decomposable entanglement witness for $3 \otimes 3$ system for some particular
choice of its parameters. By proving the optimality of the well known reduction
map and combining it with the optimal and non-decomposable 3 $\otimes$ 3 BDEW
(named critical entanglement witnesses) the family of optimal and
non-decomposable 3 $\otimes$ 3 BDEW have also been obtained. Using the
approximately critical entanglement witnesses, some 3 $\otimes$ 3 bound
entangled states are so detected. So the well known Choi map as a particular
case of the positive map in connection with this witness via Jamiolkowski
isomorphism has been considered which approximately is obtained via linear
programming.
