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In this paper, we investigate a downlink channel of a large intelligent surface (LIS) communication system. The LIS is equipped with B-bit discrete phase shifts while base station (BS) exploits low-resolution digital-to-analog converters (DACs). Without the knowledge of channel state information (CSI) related to the LIS, we propose a practical phase shift design method, whose computational complexity increases by 2 B independent of the number of reflecting elements N. A tight lower bound for the asymptotic rate of the user is obtained in closed form. As N increases, we observe that the asymptotic rate becomes saturated because both the received signal power and the DAC quantization noise increase. Compared to the optimal continuous phase shift design with perfect CSI, our proposed method asymptotically approaches the ideal benchmark performance for moderate to high values of B. The derived results and observations are verified by simulation results.