Abstract
The main result of this paper is that point sets in PG, , , , of size less than and intersecting each -space in modulo points (such point sets are always minimal blocking sets with respect to -spaces) are either -spaces or certain Baer cones. The latter ones are cones with vertex a -space, where , and with a -dimensional Baer subgeometry as a base. Bokler showed that non-trivial minimal blocking sets in PG with respect to -spaces and of size at most are such Baer cones. The corollary of the main result is that we improve on Bokler’s bound. The improvement depends on the divisors of ; for example, when is a prime square, we get that the non-trivial minimal blocking sets of PG with respect to -spaces and of size less than are Baer cones.
Citation
Zsuzsa Weiner. "Small point sets of $\mathrm{PG}(n,q)$ intersecting each $k$-space in $1$ modulo $\sqrt{q}$ points." Innov. Incidence Geom. 1 171 - 180, 2005. https://doi.org/10.2140/iig.2005.1.171
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