It is well-known that the following divisibility conditions are necessary for the existence of a t-(v, k, A) design: A(V-~) == 0 mod (k~), Os; i:::; t. t-, t-, A t.( v, k, A) design (0, £ilJ) with £ilJ =0 or ffi=Lk(n) is said to be trivial. One can show by elementary counting arguments that in a trivial t-(v, k,A) design, we must have either A=0 or A = (k=:)' The complement of a t.(v, k, A) des...