Individual neurons are noisy. Therefore, it seems necessary to pool the activity of many neurons to obtain an accurate representation of the environment. However, it is widely believed that shared noise in the activity of nearby neurons renders such pooling ineffective, limiting the accuracy of the population code and, ultimately, behavior. However, these predictions are based on extrapolating models fit to small numbers of neurons and have not been tested experimentally. Using a novel high-speed 3D-microscope we densely recorded from hundreds of neurons in the mouse visual cortex and measured the amount of information encoded. We find that the information in this sensory population increases approximately linearly with population size and does not saturate, even for several hundred neurons. This information growth is facilitated by a correlation structure that is not aligned with the tuning, making it less harmful than would be predicted from pairwise measurements. Accordingly, a decoder that accounts for the correlation structure outperforms one that does not. Our findings suggest that sensory representations may be more accurate than previously thought and therefore that psychophysical limitations may arise from downstream neural processes rather than limitations in the sensory encoding.