Let Ω and \documentclass[12pt]{minimal}
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\begin{document}$${\bar B}$$\end{document} be a subset of Σ = PG(2n−1,q) and a subset of PG(2n,q) respectively, with Σ ⊂ PG(2n,q) and \documentclass[12pt]{minimal}
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\begin{document}$${{\bar B}\not\subset \Sigma}$$\end{document}. Denote by K the cone of vertex Ω and base \documentclass[12pt]{minimal}
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\begin{document}$${\bar B}$$\end{document} and consider the point set B defined by
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\begin{document}$$B=\big(K{\setminus}\Sigma\big) \cup \{X\in \S\, : \, X\cap K\neq \emptyset\},$$\end{document}
in the André, Bruck-Bose representation of PG(2,qn) in PG(2n,q) associated to a regular spread \documentclass[12pt]{minimal}
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\begin{document}$${\cal S}$$\end{document} of PG(2n−1,q). We are interested in finding conditions on \documentclass[12pt]{minimal}
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\begin{document}$${\bar B}$$\end{document} and Ω in order to force the set B to be a minimal blocking set in PG(2,qn) . Our interest is motivated by the following observation. Assume a Property α of the pair (Ω,\documentclass[12pt]{minimal}
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\begin{document}$${\bar B}$$\end{document}) forces B to turn out a minimal blocking set. Then one can try to find new classes of minimal blocking sets working with the list of all known pairs (Ω, \documentclass[12pt]{minimal}
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\begin{document}$${\bar B}$$\end{document}) with Property α. With this in mind, we deal with the problem in the case Ω is a subspace of PG(2n−1,q) and \documentclass[12pt]{minimal}
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\begin{document}$${\bar B}$$\end{document} a blocking set in a subspace of PG(2n,q); both in a mutually suitable position. We achieve, in this way, new classes and new sizes of minimal blocking sets in PG(2,qn), generalizing the main constructions of [14]. For example, for q = 3h, we get large blocking sets of size qn + 2 + 1 (n≥ 5) and of size greater than qn+2 + qn−6 (n≥ 6). As an application, a characterization of Buekenhout-Metz unitals in PG(2,q2k) is also given.
