The problem of downlink non-orthogonal multiple access (NOMA) scheme over fast fading channels is studied. A new class of downlink NOMA scheme is proposed, where each user's signals are encoded to a constellation corresponding to the same algebraic lattices from number fields and the transmitter sends the superposition of users' signals. The minimum product distance achieved by the proposed scheme with an arbitrary power allocation factor is investigated and its upper bounds are derived. Within this class, a family of NOMA schemes based on lattice partitions of the underlying ideal lattice is identified, whose minimum product distances can be easily controlled. Numerical results show that the scheme based on lattice partitions always results in the largest possible minimum product distance among the proposed class. Simulation results further indicate that the proposed scheme significantly outperforms the conventional NOMA scheme and the current state-of-the-art.