reduced designs constructed by key-moori method 2 and their connection with method 3

For a 1-(v,k,λ) design d containing a point x, we study the set ix, the intersection of all blocks of d containing x. we use the set ix together with the key-moori method 2 to construct reduced designs invariant under some families of finite simple groups. we also show that there is a connection between reduced designs constructed by method 2 and the new moori method 3.