Blocking sets of tangent lines to a hyperbolic quadric in PG(3, 3)

Let Q+(3,q) be a hyperbolic quadric in PG(3,q) and T be the set of all lines of PG(3,q) which are tangent to Q+(3,q). If k is the minimum size of a T-blocking set in PG(3,q), then we prove that q2+1≤k≤q2+q. When q=3, we show that: (i) there is no T-blocking set of size 10, and (ii) there are exactly...

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Bibliographic Details
Published in:Discrete Applied Mathematics 2019-08, Vol.266, p.121-129
Main Authors: De Bruyn, Bart, Sahoo, Binod Kumar, Sahu, Bikramaditya
Format: Article
Language:English
Subjects:
Blocking set
Computer algebra
Conic
Hyperbolic quadric
Isomorphism
Ovoid
Projective space
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Summary:Let Q+(3,q) be a hyperbolic quadric in PG(3,q) and T be the set of all lines of PG(3,q) which are tangent to Q+(3,q). If k is the minimum size of a T-blocking set in PG(3,q), then we prove that q2+1≤k≤q2+q. When q=3, we show that: (i) there is no T-blocking set of size 10, and (ii) there are exactly two T-blocking sets of size 11 up to isomorphism. By means of the computer algebra systems GAP (The GAP Group, 2014) and Sage (Sage Mathematics Software (Version 6.3), 2014), we find that there exist no T-blocking sets of size q2+1 for each odd prime power q≤13.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2018.12.010