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

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 6blocking 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 Rdei-type exist. Second: We classify the minimal blocking sets of size 17.