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Recently a number of nonlinear precoding algorithms have been developed for designing a downlink transmit signal that is constrained by some nonlinearity, such as one-bit quantization, power-amplifier saturation or constant modulus. These methods use iterative search algorithms to directly design the signal that is transmitted from each antenna. Since the dimension of the search space equals the number of antennas, the computational complexity of these approaches can be high for massive MIMO scenarios. Thus, in this paper we pose the problem in a smaller dimensional space by constraining the signal prior to the nonlinearity to be the output of a linear precoder. The search is then over the vector of predistorted symbols at the input to the linear precoder, which is typically much smaller than the number of antennas. We focus on algorithms that minimize the bit error rate at the receivers, and show that performance can be obtained that is similar to algorithms that operate directly in the antenna domain.