Uniqueness of a projective transformation

Question

Just as there exists a unique projective transformation that takes three points in $\mathbb{CP}^1$ to three other points in $\mathbb{CP}^1$, how many points do I need for the corresponding question in $\mathbb{CP}^3$? In other words, suppose I want a projective transformation to map a set of (ordered) $n$ points in $\mathbb{CP}^3$ to another set of (ordered) $n$ points in $\mathbb{CP}^3$, what should $n$ be so that there exists a exactly one projective (linear) transformation that will do so? Do I need a condition on the configuration of the set of points? Do they have to be in linear general position or any other restriction?