A characterization of 42 ovoids with a certain property in PG(3,2)

Abstract

In this paper, we characterize 42 ovoids with a certain property in a projective space PG(3,2) described in Yucas [6]. As a corollary, we construct the Steiner 4-wise balanced design S(4,{5,6},17) with 252 blocks which is an extension of the point-plane design A of an affine space AG(4,2). The construction leads to not only the uniqueness of such an extension, but also a (usual) extension of the 2-repeated design 2.A.