Although the quest for more accurate solutions is pushing deep learning research towards larger and more complex algorithms, edge devices demand efficient inference and therefore reduction in model size, latency and energy consumption. One technique to limit model size is quantization, which implies using fewer bits to represent weights and biases. Such an approach usually results in a decline in performance. Here, we introduce a method for designing optimally heterogeneously quantized versions of deep neural network models for minimum-energy, high-accuracy, nanosecond inference and fully automated deployment on chip. With a per-layer, per-parameter type automatic quantization procedure, sampling from a wide range of quantizers, model energy consumption and size are minimized while high accuracy is maintained. This is crucial for the event selection procedure in proton-proton collisions at the CERN Large Hadron Collider, where resources are strictly limited and a latency of ${\mathcal O}(1)~μ$s is required. Nanosecond inference and a resource consumption reduced by a factor of 50 when implemented on field-programmable gate array hardware are achieved.