Simple abelian quadruple systems

We generalize a construction of simple cyclic 3-designs due to Köhler (1981) to that of simple abelian 3-designs. We prove that for any abelian group A of order v ≡ 2 ( mod 4 ) , there exists a simple 3- ( v , 4 , 3 ) design with A ⋊ Aut ( A ) as an automorphism group.