The existence of 3 pairwise additive $B(v,2,1)$ for any $v\ge 6$

Abstract

The existence of additive BIB designs and 2 pairwise additive BIB designs has been discussed with direct and recursive constructions in [6, 9]. In this paper, by reorganizing some methods of constructing pairwise additive BIB designs from other combinatorial structures, it is shown that 3 pairwise additive $B(v,2,1)$ can be constructed for any integer $v\ge 6$.