Pairwise additive 1-rotational BIB designs with lambda = 1

The existence of pairwise additive balanced incomplete block (BIB) designs and pairwise additive cyclic BIB designs with lambda = 1 has been discussed through direct and recursive constructions in the literature. This paper takes BIB designs with 1-rotational automorphisms and then the existence of pairwise additive 1-rotational BIB designs is investigated for lambda = 1. Finally, it is shown that there exists a 2-pairwise additive 1 rotational BIB design with parameters v, k and lambda = 1 if and only if any v >= 4 and k = 2.