Geodesic
Some new upper bounds for the size of partial ovoids in slim generalized polygons and generalized hexagons of order $(s,s^3)$
Journal of Algebraic Combinatorics, Tome 12 (2000) no. 2, pp. 107-113.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: From an elementary observation, we derive some upper bounds for the number of mutually opposite points in the classical generalized polygons having 3 points on each line. In particular, it follows that the Ree-Tits generalized octagon $O(2)$ of order (2, 4) has no ovoids. Also, we deduce from another observation a similar upper bound in any generalized hexagon of order $( s, s ^{3})$.
Keywords: generalized polygon, generalized hexagon, ovoid, partial ovoid, projective embedding 
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     title = {Some new upper bounds for the size of partial ovoids in slim generalized polygons and generalized hexagons of order $(s,s^3)$},
     journal = {Journal of Algebraic Combinatorics},
     pages = {107--113},
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     year = {2000},
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Coolsaet, Kris; Van Maldeghem, Hendrik. Some new upper bounds for the size of partial ovoids in slim generalized polygons and generalized hexagons of order $(s,s^3)$. Journal of Algebraic Combinatorics, Tome 12 (2000) no. 2, pp. 107-113. http://geodesic.mathdoc.fr/item/JAC_2000__12_2_a6/