Tracking detectors capable of recording the hit-time information at a precision of O(10 ps) will be breakthrough devices in the future of hadron collider experiments to resolve signal tracks in a harsh environment with significant background tracks. The low-gain avalanche detector (LGAD) is an example of such a device, which is expected to provide real-time fine spatial resolution for a 4-D tracking detector. In this study, we have fabricated LGAD diodes and segmented strip-type detectors at Hamamatsu Photonics. We tested pad type detectors using a proton beam and obtained a time resolution better than 30 ps for the devices with an active thickness of 50 $\mu$m. The non-uniformity of the gain across the strip was modeled using TCAD simulation, which was then used to design segmented LGAD sensors with a uniform gain. The study suggests that uniform LGAD sensors can be made with a broader operation bias voltage range. In this paper, we present the test beam and the TCAD simulation results.