Complete classification in characteristic three

Obtain a full classification of degree-three ovoids O₇(f₁,f₂,f₃) of Q⁺(7,q) when the underlying field has characteristic p = 3.

Background

The degree-three analysis treats the case p = 3 separately. The authors derive partial results using methods analogous to those used for p > 3, but do not obtain a complete classification.

Consequently, the structure of all degree-three ovoids parameterized by triples f₁,f₂,f₃ in characteristic three remains unresolved.

References

However, obtaining a complete classification forO7(f1, f2, f3) in this scenario proved to be challenging, and we leave this as an open problem. Open Problem 5.7. Obtain a full classification for ovoids O7(f1, f2, f3) of degree 3 whenp = 3.

— Ovoids of $Q^+(7,q)$ of low-degree  (2502.02219 - Bartoli et al., 4 Feb 2025) in Open Problem 5.7, Section 5.2.3, p. 21