Neurons in an area of the mammalian brain, the medial entorhinal cortex, fire only when the animal is located in particular positions in its environment. Remarkably, these locations are arranged geometrically in a hexagonal lattice that tiles the plane. Thus these neurons, which were discovered in 2005, are called grid cells. The joint activity of many such cells forms a representation of the animal's location. It has been hypothesized that this representation is optimized to represent position with high accuracy, while constraining the number of participating neurons. Recent experiments established that grid cells are functionally organized in sets (called modules) that share the same lattice periodicity, where the periodicities are discrete. The cells within the same module differ from each other by spatial translation. The periodicities associated with all modules approximately form a geometric series. This result is in agreement with recent theories, which postulate that grid cells implement an efficient coding scheme for the animal’s position. However, the experimental data suggests also that the number of cells decreases sharply with module periodicity, in marked disagreement with existing theories. Here, we postulate that the entorhinal cortex is adapted to represent a dynamic quantity (the trajectory of the animal in space), while taking into account the temporal statistics of this variable. We first develop a theory for efficient coding of a variable that dynamically follows the statistics of a simple random walk. We optimize the resolution of the animal’s location readout from the grid cells, while constraining the total number of cells. A central prediction of the theory is that module neuron population sizes should sharply decrease with the increase of module periodicities, in agreement with the trends seen in the experimental data. Another prediction is that the ratio between the periodicities should approach a constant value in the modules with the smallest periodicities, which is consistent with experimental data and with previously proposed models. Next, we identify a remarkably simple, near optimal scheme for readout of the grid cell code by neural circuitry, in which the spikes from grid cells are linearly summed using an exponential temporal kernel, whose decay time depends on the module periodicity. Finally, we abandon the assumption of a simple random walk, and show that our qualitative predictions hold under a wide range of assumptions on the statistics of motion of the animal. Thus, we propose that the sharp decrease in module population sizes, with increase of lattice periodicity, is an outcome of an optimization of resolution by a neural system in the brain, if the dynamic nature of motion in space is taken into account.