Simple 8-(31,12,3080), 8-(40,12,16 200) and 8-(40,12,16 520) designs from PSL(3, 5) and PSL(4, 3)

We show the existence of simple 8-(31,12,3080), 8-(40,12,16 200) and 8-(40,12,16 520) designs and list for each parameter set one example in full detail. The designs are constructed with a prescribed group of automorphisms PSL(3,5)PSL(3,5) or PSL(4,3)PSL(4,3) using the method of Kramer and Mesner [t-designs on hypergraphs, Discrete Math. 15 (3) (1976) 263–296].