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

Abstract

It is shown that for \(2 \leq t \leq n-3\), a strict \(t\)-SB\((n,n-1)\) design does not exist, but for \(n \geq 3\), 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.