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Multiple Blocking Sets and Arcs in Finite Planes
Author(s) -
Ball Simeon
Publication year - 1996
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/54.3.581
Subject(s) - blocking (statistics) , upper and lower bounds , combinatorics , mathematics , value (mathematics) , set (abstract data type) , blocking set , prime (order theory) , geometry , mathematical analysis , computer science , pure mathematics , statistics , complex projective space , projective test , projective space , programming language
This paper contains two main results relating to the size of a multiple blocking set in PG(2, q ). The first gives a very general lower bound, the second a much better lower bound for prime planes. The latter is used to consider maximum sizes of ( k , n )‐arcs in PG(2, 11) and PG(2, 13), some of which are determined. In addition, a summary is given of the value of m n (2, q ) for q ⩽ 13.