Develop stronger constructions and bounds for covering-sequence codes

Develop new constructions that improve the upper bounds for the parameters in Table I where the interleaving construction is weak, and derive upper bounds on the sizes of covering-sequence codes.

Background

Several upper bounds in Table I are obtained through the interleaving construction, which the paper characterizes as relatively weak for many parameter choices. The authors seek alternatives comparable in strength to Construction 3 and also identify the absence of corresponding upper bounds for covering-sequence codes as an unresolved issue.

References

  1. Many of the upper bounds used in Table I are quite weak as Construction 2 is used and we do not have for these parameters a stronger construction like Construction 3. We would like to see some new constructions that will make the table more balanced. Similarly, we want to see upper bounds on the sizes of covering sequence codes.
— Constructions of Covering Sequences and Arrays  (2502.08424 - Chee et al., 12 Feb 2025) in Section VIII, Conclusion and Future Research, Problem 2