Geodesic
Blocking Sets and Skew Subspaces of Projective Space
Canadian journal of mathematics, Tome 32 (1980) no. 3, pp. 628-630

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In what follows, a theorem on blocking sets is generalized to higher dimensions. The result is then used to study maximal partial spreads of odd-dimensional projective spaces. Notation. The number of elements in a set X is denoted by |X|. Those elements in a set A which are not in the set Bare denoted by A — B. In a projective space Σ = PG(n, q) of dimension n over the field GF(q) of order q, ┌d(Ωd, Λd, etc.) will mean a subspace of dimension d. A hyperplane of Σ is a subspace of dimension n — 1, that is, of co-dimension one.A blocking set in a projective plane π is a subset S of the points of π such that each line of π contains at least one point in S and at least one point not in S. The following result is shown in [1], [2]. 
Bruen, Aiden A. Blocking Sets and Skew Subspaces of Projective Space. Canadian journal of mathematics, Tome 32 (1980) no. 3, pp. 628-630. doi: 10.4153/CJM-1980-048-8
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[1] 1. Bruen, A., Baer subplanes and blocking sets, Bull. Amer. Math. Soc. 76 (1970), 342–344. Google Scholar

[2] 2. Bruen, A., Blocking sets infinite projective planes, SIAM. J. Appl. Math. 21 (1971), 380–392. Google Scholar

[3] 3. Bruen, A., Collineations and extensions of translation nets, Math. Z. 145 (1975), 243–249. Google Scholar

[4] 4. Bruen, A. and Thas, J. A., Blocking sets, Geom. Ded. 6 (1977), 193–203. Google Scholar

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