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When performed using an exhaustive search, the maximum likelihood (ML) joint detection of all users in a multi-carrier code division multiple access (MC-CDMA) system has a prohibitive complexity, growing exponentially with the number of users and the number of bits in each modulation symbol. An ML multiuser detection algorithm has previously been proposed, with a complexity growing polynomially with the number of users, independent of the modulation size. The MC-CDMA system is modelled as a sphere packing lattice and a low-complexity optimum lattice decoder, called the sphere decoder, is applied to jointly detect all users. We propose sub-optimum simplifications, based on orthogonal projection of the received signal on a facet of the lattice constellation, to further decrease the complexity. Simulation results are shown with up to 64 users transmitting 16-QAM symbols.