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

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 \( v \geq 6 \).