Determination of the smallest larger nontrivial blocking-set size

Determine the value of δ′, defined by requiring that p^3+δ′ be the cardinality of the smallest non-trivial minimal blocking set in PG(2,p^3) whose cardinality exceeds p^3+p^2+p+1, for p=p_0^h with p_0≥7 prime and h>1.

Background

In the final part of the paper, results about small minimal blocking sets in projective planes are transferred to Cameron–Liebler sets on the Klein quadric through the correspondence with holes of maximal partial line spreads in PG(3,q). For q=p^3, the parameter δ′ is used to define a threshold δ_0 governing classification results for such holes and the associated Cameron–Liebler sets.

The quantity δ′ concerns the first cardinality above the known projected-subgeometry size p^3+p^2+p+1 at which a non-trivial minimal blocking set can occur. The paper states that this value is not known, while recording the upper bound δ′≤p^3/p_0+1. Resolving δ′ would sharpen the range in which the paper’s structural classifications apply.