The success of fMRI places constraints on the nature of the neural code. The fact that researchers can infer similarities between neural representations, despite limitations in what fMRI measures, implies that certain neural coding schemes are more likely than others. For fMRI to be successful given its low temporal and spatial resolution, the neural code must be smooth at the subvoxel and functional level such that similar stimuli engender similar internal representations. Through proof and simulation, we evaluate a number of reasonable coding schemes and demonstrate that only a subset are plausible given both fMRI's successes and its limitations in measuring neural activity. Deep neural network approaches, which have been forwarded as computational accounts of the ventral stream, are consistent with the success of fMRI, though functional smoothness breaks down in the later network layers. These results have implications for the nature of neural code and ventral stream, as well as what can be successfully investigated with fMRI.