On the blocking sets in S(3,6,22) and S(4,7,23)

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.