The fundamental combinatorial structure of a net in $ℂP^2$ is its associated set of mutually orthogonal Latin squares. We define equivalence classes of sets of orthogonal Latin squares by label equivalences of the lines of the corresponding net in $ℂP^2$. Then we count these equivalence classes for small cases. Finally we prove that the realization spaces of these classes in $ℂP^2$ are empty to show some non-existence results for 4-nets in $ℂP^2$.