Successful processing of millisecond scale motion information is crucial for survival. Here, we show that, in the blowfly’s visual system, efficient stimuli encoding emerges at the earliest stage of global motion perception to cope with this challenge. Moreover, the uniquely strong axonal gap junctions (GJ) in this circuit are essential for achieving such near optimal efficiency. We focus on the VS network in the lobula plate of the blowfly’s compound eyes. It consists of 10 vertical sensitive (VS) cells (VS1-VS10), each set tiling the visual world of a given hemisphere. This network integrates responses from a large set of local motion detectors and sends the resulting global motion-sensitive signal to downstream descending neurons which in turn target neck and wing muscles for head and body movements, respectively. This VS network is designated to encode rotational motion, i.e., the rotational axis $\theta$, with an intriguing structure: first, each VS cell connects with neighboring cells via strong (~$1\mu S$) axonal gap junctions. Second, only subpopulations on both sides connect with downstream pathways, i.e., only the VS5,6,7 send output to the descending premotor neurons. Previous work [Trousdale et.al, J. Neuroscience, 2014] shows that with GJs, this subpopulation encoding can successfully estimate the horizontal $\theta$. What makes the presence of GJs so helpful? By modeling the VS network, we find that these strong GJs help the VS5,6,7 encoding to obtain at least 90% efficiency as compared to the theoretical physical limit, determined by the input statistics, for both natural and checkerboard stimuli. When estimating $\theta$ (with the natural stimuli), the VS5,6,7 encoding can represent both axes (‘roll’ and ‘pitch’) successfully with GJs as opposed to only one axis (‘roll’) without GJs. When discriminating between $\theta$ and $\theta’$ (with the checkerboard stimuli), hyperacuity emerges in the presence of strong GJs.