Largest minimal blocking sets in PG(2,8)

Abstract

AbstractBruen and Thas proved that the size of a large minimal blocking set is bounded by $q \cdot {\sqrt{q}} + 1$. Hence, if q = 8, then the maximal possible size is 23. Since 8 is not a square, it was conjectured that a minimal blocking 23‐set does not exist in PG(2,8). We show that this is not the case, and construct such a set. We prove that this is combinatorially unique. We also complete the spectrum problem of minimal blocking sets for PG(2,8) by showing a minimal blocking 22‐set. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 162–169, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10035