Geodesic
On minimal blocking sets of the generalized quadrangle $Q(4, q)$
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) (2005).

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The generalized quadrangle $Q(4,q)$ arising from the parabolic quadric in $PG(4,q)$ always has an ovoid. It is not known whether a minimal blocking set of size smaller than $q^2 + q$ (which is not an ovoid) exists in $Q(4,q)$, $q$ odd. We present results on smallest blocking sets in $Q(4,q)$, $q$ odd, obtained by a computer search. For $q = 5,7,9,11$ we found minimal blocking sets of size $q^2 + q - 2$ and we discuss their structure. By an exhaustive search we excluded the existence of a minimal blocking set of size $q^2 + 3$ in $Q(4,7)$. 
@article{DMTCS_2005_special_250_a75,
     author = {Cimr\'akov\'a, Miroslava and Fack, Veerle},
     title = {On minimal blocking sets of the generalized quadrangle $Q(4, q)$},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)},
     year = {2005},
     doi = {10.46298/dmtcs.3466},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3466/}
}
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%J Discrete mathematics & theoretical computer science
%D 2005
%V DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
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Cimráková, Miroslava; Fack, Veerle. On minimal blocking sets of the generalized quadrangle $Q(4, q)$. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) (2005). doi : 10.46298/dmtcs.3466. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3466/

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