Construct stronger covering arrays and lower bounds

Construct additional covering arrays and establish lower bounds on the size of (m × n, R)-covering arrays.

Background

The paper generalizes covering sequences to doubly periodic covering arrays and presents folding and shift-based constructions. These constructions provide upper bounds, but the authors identify the need for both further construction methods and lower bounds governing the minimum area or size of covering arrays.

References

We can avoid this if $B$ contains a symmetric $k\times k$ submatrix, but it is not clear to us that this is necessarily the case. (It may be an interesting problem to find conditions under which $B$ necessarily contains a symmetric $k\times k$ submatrix.)

— The VC-dimension of strongly regular graphs  (2609.10330 - Byrne et al., 9 Sep 2026) in Section 3, subsection The case n\ge 3
  1. We would like to see more constructions as well as lower bounds on the size of covering arrays.
— Constructions of Covering Sequences and Arrays  (2502.08424 - Chee et al., 12 Feb 2025) in Section VIII, Conclusion and Future Research, Problem 4