Exact maximal binary rank at real rank six

Determine the exact value of the maximal binary rank b_6 among 0,1 matrices of real rank 6, beyond the upper bound established in the paper.

Background

The paper defines b_d as the maximal binary rank possible for a 0,1 matrix with real rank d. It establishes the exact values b_3=4, b_4=6, and b_5=9, while proving only the upper bound b_6≤17. The exact extremal value for real rank six is therefore left unresolved.

References

Another interesting open problem is to find the exact value of $b_6$ since we give only an upper bound of $b_6$.

— On the Binary Rank of Matrices with Constant Real Rank  (2609.30203 - Parnas, 24 Sep 2026) in Introduction, subsection “Our results”