Some new 3-designs from PSL(2, q) with q ≡ 1 (mod4).

We determine the sizes of orbits from the action of subgroups of PSL(2, q) on projective line X = GF( q) ∪ {∞} with q a prime power and congruent to 1 modulo 4. As an example of its application, we construct some new families of simple 3-designs admitting PSL(2 , q) as automorphism group. [ABSTRACT FROM AUTHOR]