Motivated by challenges to existing multiuser transmission methods in a low signal to noise ratio (SNR) regime, and emergence of massive numbers of low data rate ehealth and internet of things (IoT) devices, in this paper we show that it is beneficial to incorporate knowledge of modulation type into multiuser transmit precoder design. Particularly, we propose a transmit precoding (beamforming) specific to BPSK modulation, which has maximum power efficiency and capacity in poor channel conditions. To be more specific, in a multiuser scenario, an objective function is formulated based on the weighted sum of error probabilities of BPSK modulated users. Convex optimization is used to transform and solve this ill-behaved non-convex minimum probability of error (MPE) precoding problem. Numerical results confirm significant performance improvement. We then develop a low-complexity user selection algorithm for MPE precoding. Based on line packing principles in Grassmannian manifolds, the number of supported users is able to exceed the number of transmit antennas, and hence the proposed approach is able to support more simultaneous users compared with existing multiuser transmit precoding methods.