Notes on Semiarcs

On the Structure of Semiovals of Small Size

“…In Section 2, some results on the nonexistence of semiovals of small size are given. In Section 3, search results on the classification of semiovals in PG (2,8) and PG (2,9) are presented. In Section 4, new theoretical results on the structure of semiovals containing a (q − 1)-secant are presented.…”

“…In this section, the search results on the classification of semiovals in PG (2,8) and PG (2,9) are presented.…”

“…r The semioval S 23 of size 23 has two points lying on one bisecant and seven 4-secants, and 21 points lying on two trisecants and six 4-secants; its stabilizer group acts transitively on these 21 points and fixes the other two. The spectrum of semiovals in PG (2,9) has been determined in [23]. The semiovals S in PG (2,9) of size less than or equal to 16 have been classified by computer search.…”

“…The spectrum of semiovals in PG (2,9) has been determined in [23]. The semiovals S in PG (2,9) of size less than or equal to 16 have been classified by computer search. Explicit examples of semiovals in PG (2,9) of size less than or equal to 16 and information on the stabilizer groups can be found in [2].…”

“…Let be a projective plane of order q . A semioval in is a nonempty pointset with the property that for every point there exists a unique line such that (see e.g., ). This line is called the tangent line to at P .…”