A new family of BIBDs and non-embeddable (16,24,9,6,3)-designs (Q1823247)

When a block from a symmetric 2-(V,K,\(\lambda)\) design is removed, one gets a 2-(v,k,\(\lambda)\) design satisfying \(r=k+\lambda\). The question is which 2-(v,k,\(\lambda)\) designs with \(r=k+\lambda\) are obtained in this way; those designs are called embeddable. The first non-embeddable design was a 2-(16,6,3) design constructed by \textit{K. N. Battacharya} [A new balanced incomplete block design, Sci. Culture 9, 508 (1944)]. In the paper under review, the author constructs 251 non-embeddable 2-(16,6,3) designs and shows that the number of (non-isomorphic) 2-(16,6,3) designs is at least 1542.