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

• Main Authors: Chanar Abdulkareem Ahmed, AbdulKhlaq Lazem Yaseen
• Format: Article
• Language: Arabic
• Published: College of Education for Pure Sciences 2009-06-01
• Series: مجلة التربية والعلم
• Subjects: template groups pg(2; q); minimum; 16&17 pg(2; 9)
• Online Access: https://edusj.mosuljournals.com/article_57688_130b44296ccaaabb53ab78bb06ca43b7.pdf
• ISSN: 1812-125X; 2664-2530

Abstract<br /> 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.<br /> 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.<br /> 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.<br /> Specially in the projective plane PG(2, 9):<br /> 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.<br /> Second: We classify the minimal blocking sets of size 17.