Exact rectangle covering number for the regular 35-gon

Determine the exact rectangle covering bound for the slack matrix of the regular 35-gon.

Background

The paper computes the rectangle covering bound (RCB) for regular polygon slack matrices through n=33 and notes that the exact value for n=35 is the next unresolved RCB value. Resolving it would extend the known sequence of exact combinatorial lower bounds, although the authors state that it would not currently provide new information about the non-negative rank because a stronger lower bound is already known.

References

The exact value of $n=35$ remains open, but does not deliver new information on the $r_+$, because the best known lower bound is bigger.

— Computing Lower Bounds on the Non-negative Rank via SAT Solvers  (2610.11950 - Engel et al., 8 Oct 2026) in Section 5, subsection “Known Values of Lower Bounds and the Non-negative Rank”; Section 6, Conclusion