In this paper, we propose a new Motion Estimation algorithm based on low discrepancy sequences, essentially quasi-random sequences used as point sampling to compute multivariate integral approximations by methods such as Monte-Carlo. Our evaluation of the proposed method took into consideration PSNR mean values, computational effort and bit-rate. The results support that the proposed algorithm entitled Quasi-Random Search (QRS) is able to significantly reduce computational effort by 73,06% in average when compared to the UMHS algorithm while maintaining video quality and a slight increase in the bit-rate.