Three families of multiple blocking sets in Desarguesian projective planes of even order (Q1952273)

If \(H\) is a hyperoval of \(\mathrm{PG}(2,2^h),\) denote with \(\mathcal E\) the set of all lines external to \(H\) and with \(\mathcal S\) the set of all lines secant to \(H\). Using such sets of lines, the authors define three different families of lines \({\mathcal A}_1,\) \({\mathcal A}_2\) \({\mathcal A}_3\) of \(\mathrm{PG}(2,2^h)\) whose dual is a \(k\)-arc. As the complement of a \(k\)-arc is an \(s\)-fold blocking set with \(s+k=2^h+1,\) they construct three examples of multiple blocking sets. The first and the third construction only apply to translation hyperovals.