Dual Reed–Muller 3-design conjecture. If q≥3q\geq 3q≥3, then for every ℓ∈N\ell\in\mathbb{N}ℓ∈N, (C⊥)ℓ(C^{\perp})_{\ell}(C⊥)ℓ is not a combinatorial 333-design.
