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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 thebinary 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 30,264nonisomorphic quasi-symmetric 2-$(64,24,46)$ designs obtainable from maximalarcs in $AG(2,2^2)$ via the Blokhuis-Haemers construction. The related stronglyregular graphs are also discussed.

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