Lower bounds for VC-dimension of general orthogonal arrays

Generalize the lower bound for the VC-dimension of Latin square graphs to graphs of general orthogonal arrays.

Background

The paper proves an upper bound of k(k-1) for the VC-dimension of graphs arising from OA(k,m), and notes that some families have unbounded VC-dimension. However, the authors explicitly state that they were unable to extend the lower-bound argument used for Latin square graphs to arbitrary orthogonal arrays.

References

We were not even able to generalize the lower bound in Theorem \ref{Theorem Latin square} to general orthogonal arrays.

— The VC-dimension of strongly regular graphs  (2609.10330 - Byrne et al., 9 Sep 2026) in Section 5, subsection Orthogonal arrays