This thesis documents the development of all possible non-isomorphic 3-(12,6,4) and 2-(11,5,4) designs. A representative copy of each of the 545 non-isomorphic 3-(12,6,4) designs along with all its non-trivial automorphisms is given. The point orbits of these designs can then be used to produce a copy of any of the 4393 non-isomorphic 2-(11,5,4) designs found to occur.