Metamorphosis of simple twofold triple systems into twofold (K4-e)(K4-e)-designs

Abstract In this note, we show that there exists a metamorphosis of a simple twofold triple system of order v into a twofold ( K 4 − e ) -design of order v if and only if v ≡ 0 , 1 , 6 , 10 ( mod 15 ) and v ⩾ 10 .