Improvement of the classification inequality

Improve the inequality q ≥ 4n² − 8n + 2 in the theorem asserting that a good pseudo-ovoid in PG(4n − 1, q) for odd q is classical or of Kantor–Knuth type.

Background

For odd q, the cited theorem shows that a good pseudo-ovoid satisfying q ≥ 4n² − 8n + 2 must be classical or of Kantor–Knuth type. The paper explicitly identifies improving this numerical hypothesis as an open problem, with the aim of extending the classification to smaller field orders.