On the existence of blocking 3-sets in designs

AbstractThe only 2−(v,k,λ) designs with r⩾2λ and k⩾λ in which a minimal blocking 3-set may exist are the following: a 2−(2λ+3,λ+1,λ) design with λ⩾3; a 2−(2λ+2,λ+1,λ) design with λ⩾3; a 2−(2λ−1,λ,λ) design with λ⩾4; a 2−(4λ+3,2λ+1,λ) Hadamard design with λ⩾3; a 2−(4λ−1,2λ+1,λ) Hadamard design with λ⩾2; see L. Berardi (A note on 3-blocked designs, J. Combin. Designs 5 (1) (1997) 61–69). Moreover, in Berardi (1997) the case of Hadamard designs has been studied. In this paper we deal with the problem of the existence of blocking 3-sets in the remaining designs