Determine the smallest unresolved blocking-set size parameter

Determine the value of δ' for q=p^3, where p=p_0^h with p_0≥7 prime and h>1, such that p^3+δ' is the cardinality of the smallest non-trivial minimal blocking set in PG(2,p^3) having cardinality larger than p^3+p^2+p+1.

Background

In the discussion of maximal partial spreads in PG(3,p3), the paper defines a threshold δ_0 using δ'. The parameter δ' measures the size gap between the known projected-subgeometry examples and the smallest larger non-trivial minimal blocking set in PG(2,p3).

The authors state that δ' is currently unknown, although they give the upper bound δ'≤p3/p_0+1. Resolving δ' would sharpen the range in which the subsequent structural classification of holes, and therefore the corresponding Cameron–Liebler sets on the Klein quadric, applies.

References

Presently, this value is still unknown, but we know $\delta' \leq p3/p_0+1$.

— Cameron-Liebler sets of generators in the Klein quadric $Q^+(5,q)$  (2503.08260 - D'haeseleer et al., 11 Mar 2025) in Section 5, notation preceding Theorem 5.?? (the definition of δ_0 before Theorems final1 and final2)