On resolvable Steiner 2-designs and maximal arcs in projective planes

A combinatorial characterization of resolvable Steiner 2-(v, k, 1) designs embeddable as maximal arcs in a projective plane of order (v−k)/(k−1) is proved, and a generalization of a conjecture by Andries Brouwer (Geometries and groups, Springer, Heidelberg, 1981) is formulated