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Scheduling in a broadcast channel based on partial channel-state-information at the transmitter is carried out in an opportunistic way. In this paper, the number of generated beams is larger than the number of available base station antennas, where the beams are obtained through Grassmannian line packing to guarantee the largest orthogonality among them. Approximate expressions and bounds are derived for the sum capacity of the proposed approach together with its scaling law. For practical systems, we show that this scheme can increase the number of serviced users under a minimum-rate-per-user requirement.