Abstract
A simple counting argument is used to show that for all q, an André hyper-regulus \({\mathbb {X}}\) in \(\mathrm{PG}(5,q)\) has exactly two switching sets. Moreover, there are exactly \(2(q^2+q+1)\) planes in \(\mathrm{PG}(5,q)\) that meet every plane of \({\mathbb {X}}\) in a point, namely the planes in the switching sets.
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Barwick, S.G., Jackson, WA. Hyper-reguli in PG(5,\(\varvec{q}\)). J. Geom. 108, 1083–1084 (2017). https://doi.org/10.1007/s00022-017-0396-9
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DOI: https://doi.org/10.1007/s00022-017-0396-9