On blocking semiovals with an 8-secant in projective planes of order 9
NAKAGAWA, Nobuo ; SUETAKE, Chihiro
Hokkaido Math. J., Tome 35 (2006) no. 1, p. 437-456 / Harvested from Project Euclid
Let $S$ be a blocking semioval in an arbitrary projective plane $\Pi$ of order 9 which meets some line in 8 points. According to Dover in $[2]$, $20\leq \vert S\vert\leq 24$. In $[8]$ one of the authors showed that if $\Pi$ is desarguesian, then $22\leq\vert S\vert\leq 24$. In this note all blocking semiovals with this property in all non-desarguesian projective planes of order 9 are completely determined. In any non-desarguesian plane $\Pi$ it is shown that $21\leq \vert S\vert \leq 24$ and for each $i\in \{ 21,22,23,24\}$ there exist blocking semiovals of size $i$ which meet some line in 8 points. Therefore, the Dover's bound is not sharp.
Publié le : 2006-05-15
Classification:  blocking semioval,  projective plane,  ternary function,  finite field,  collineation group,  51E20
@article{1285766364,
     author = {NAKAGAWA, Nobuo and SUETAKE, Chihiro},
     title = {On blocking semiovals with an 8-secant in projective planes of order 9},
     journal = {Hokkaido Math. J.},
     volume = {35},
     number = {1},
     year = {2006},
     pages = { 437-456},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1285766364}
}
NAKAGAWA, Nobuo; SUETAKE, Chihiro. On blocking semiovals with an 8-secant in projective planes of order 9. Hokkaido Math. J., Tome 35 (2006) no. 1, pp.  437-456. http://gdmltest.u-ga.fr/item/1285766364/