Cortical networks exhibit 'global oscillations', where neural spikes are entrained to an underlying oscillatory rhythm, but where individual neurons fire irregularly. While the network dynamics underlying global oscillations are well characterised, their function is debated. Here, we show that such global oscillations are a direct consequence of optimal efficient coding in spiking networks with synaptic delays. To avoid firing unnecessary spikes, neurons must share information about the network state. Ideally, membrane potentials should be correlated and reflect a 'prediction error' while spikes themselves are uncorrelated and occur rarely. We show that the most efficient representation is achieved when: (i) spikes are entrained to a global Gamma rhythm (implying a consistent representation of the error); but (ii) few neurons fire on each cycle (implying high efficiency), while (iii) excitation and inhibition are tightly balanced. This suggests that cortical networks exhibiting such dynamics are tuned to achieve a maximally efficient population code.