الحدود الدنيا للمجاميع القالبية-t في PG)‎ 2, q)‎ و إيجاد المجاميع القابلية الأصغرية ذات حجوم 16 و 17 في PG)‎2, 9)‎

الملخص EN

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 q 10in 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.