Classification of quasi-symmetric 2-(64,24,46) designs of Blokhuis-Haemers type

Abstract

This paper completes the classification of quasi-symmetric 2-$(64,24,46)$ designs of Blokhuis-Haemers type supported by the dual code $C^{\perp}$ of the binary linear code $C$ spanned by the lines of $AG(3,2^2)$ initiated in \cite{bgr-vdt}. It is shown that $C^{\perp}$ contains exactly 30,264 nonisomorphic quasi-symmetric 2-$(64,24,46)$ designs obtainable from maximal arcs in $AG(2,2^2)$ via the Blokhuis-Haemers construction. The related strongly regular graphs are also discussed.