A Non-Existence Result and Large Sets for Sarvate-Beam Designs

Abstract

It is shown that for $2\le t\le n-3$, a strict $t$-SB$(n,n-1)$ design does not exist, but for $n\ge 3$, a non-strict $2$-SB$(n,n-1)$ design exists. The concept of large sets for Steiner triple systems is extended to SB designs and examples of large sets for SB designs are given.