Equivalence classes of Latin squares and nets in CP2
Abstract
The fundamental combinatorial structure of a net in CP2 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 CP2. Then we count these equivalence classes for small cases. Finally, we prove that the realization spaces of these classes in CP2 are empty to show some non-existence results for 4-nets in CP2.
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