We investigate nonlinear precoding techniques for a multiuser multiple-input-multiple-output (MU-MIMO) downlink. When assuming full knowledge of the channel state information (CSI) at the transmitter, a vector perturbation (VP), based on sphere encoding, is a promising precoding scheme that approaches sum capacity while using a simple receiver. However, its encoding complexity can exponentially increase with the number of transmit antennas. This paper proposes a new VP scheme based on line encoding (LE), which provides very low complexity as well as competent throughput performance. For this purpose, the proposed LE scheme finds the smallest set of candidate vectors, including the optimal perturbation vector with high probability.