On Unitals with Many Baer Sublines

We identify the points of PG(2, q) with the directions of lines in GF(q3), viewed as a 3dimensional affine space over GF(q). Within this framework we associate to a unital in PG(2, q) a certain polynomial in two variables, and show that the combinatorial properties of the unital force certain restrictions on the coefficients of this polynomial. In particular, if q = p2 where p is prime then we show that a unital is classical if and only if at least (q - 2) q secant lines meet it in the points of a Baer subline.

• Type: Journal
• Year: 1999
• Where: DCC
• Authors: Simeon Ball, Aart Blokhuis, Christine M. O'Keefe
• Keywords: 3dimensional Affine Space, Computer Graphics, DCC 1999, Force Certain Restrictions, Unital