Smallest non-trivial minimal blocking set beyond the known types

Determine the value of δ′ such that p^3+δ′ is the cardinality of the smallest non-trivial minimal blocking set in PG(2,p^3) whose cardinality exceeds p^3+p^2+p+1.

Background

For q=p^3, the paper defines a parameter δ0 using the smallest non-trivial minimal blocking set whose size is larger than the known size p^3+p^2+p+1. This threshold is used in cited theorems describing holes of maximal partial spreads in PG(3,p^3), and consequently in the classification of certain Cameron–Liebler sets on Q^+(5,p^3).

The authors explicitly state that the relevant value is unknown, although an upper bound δ′≤p^3/p0+1 is available when p=p0^h with p0≥7 prime. Thus the unresolved issue is a concrete extremal blocking-set size, not merely a general direction for future work.