Weak*-topology and weak* convergence in Goldstine Theorem

Question

According to Goldstine Theorem, the unit ball of $c_0(\mathbb N)$ is weak star dense in the unit ball of $\ell^\infty(\mathbb N)$. If $f$ would be in the unit ball of $\ell^\infty(\mathbb N)$, what net in the unit ball of $c_0(\mathbb N)$ can be given that converges to $f$?

Can we give the net $\{e_i\}$?