Goodness of pseudo-ovoids and their translation duals

Determine whether every pseudo-ovoid or its translation dual is good.

Background

A pseudo-ovoid is good at an element when every (3n − 1)-space containing that element and at least two other elements contains exactly qn + 1 elements of the pseudo-ovoid. Every known pseudo-ovoid or its translation dual is good, but universality of this property is unresolved.

References

Open problem 10. Is every pseudo-ovoid or its translation dual good?

Arcs, Caps and Generalisations in a Finite Projective Space  (2503.06243 - Hirschfeld et al., 8 Mar 2025) in Open problem 10, Section 8.6, page 8