On the blocking sets in $\text{S(3,6,22)}$ and $\text{S(4,7,23)}$

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 $\text{S(3,6,22)}$ there is exactly one blocking set having size nine, and in $\text{S(4,7,23)}$ there is exactly one minimal blocking set having six points on a block.