Minimum template groups in PG(2,q) and finding minimum template groups size 16&17 in PG(2,9)

Abstract

Abstract A t – blocking set B in a projective plane PG(2, q) is a set of points such that each line in PG(2, q) contains at least t points of B and some line contains exactly t points of B. A t – blocking set B is minimal or irreducible when no proper subset of it is a t – blocking set. In particular when t = 1 then B is called a blocking set. In this paper, we find the lower bounds of the 5 – blocking set and the 6–blocking set In the projective plane PG(2, q), where q square, Then we improved the lower bound of 5– blocking set when in the same plane. Specially in the projective plane PG(2, 9): First: We show that the minimal blocking set of size 16 with a 6 – secant and the minimal blocking set of the same size of Rédei-type exist. Second: We classify the minimal blocking sets of size 17.

Keywords

• template groups pg(2
• q)
• minimum
• 16&17 pg(2
• 9)