Smallest non-trivial minimal blocking set above the projected-subgeometry size

Determine the value of δ′, where p=p_0^h with p_0≥7 and the smallest non-trivial minimal blocking set in PG(2,p^3) having cardinality larger than p^3+p^2+p+1 has cardinality p^3+δ′.

Background

The paper invokes results on minimal blocking sets in projective planes to obtain structural classifications of holes of maximal partial spreads, and then transfers those results to Cameron–Liebler sets on the Klein quadric. For q=p^3, the parameter δ′ measures the excess over p^3 in the size of the smallest non-trivial minimal blocking set whose size exceeds the known projected-subgeometry value p^3+p^2+p+1.

The exact value of δ′ is needed in the definition of the threshold δ_0 governing the subsequent classification theorems. The paper records an upper bound but explicitly states that the value itself is not known, so the associated classification range is not fully explicit.