On the blocking sets in [formula omitted] and [formula omitted

Abstract

The aim of this short note is to prove the uniqueness of certain blocking sets studied in Berardi (Ann. Discrete Math. 37 (1988) 31–42; J. Inf. Opti. Sci. 2 (1988) 263–298). Precisely, starting from a characterization contained in Berardi (1988) we prove that, up to isomorphism, in S(3,6,22) there is exactly one blocking set having size nine, and in S(4,7,23) there is exactly one minimal blocking set having six points on a block.