Fractional factorial designs are widely used in practice and typically chosen according to the minimum aberration criterion. A sequential algorithm is developed for constructing efficient fractional factorial designs. A construction procedure is proposed that only allows a design to be constructed from its minimum aberration pro jection in the sequential build-up process. To efficiently identify nonisomorphic designs, designs are divided into different categories according to their moment pro jection patterns. A fast isomorphism check procedure is developed by matching the factors using their delete-one-factor pro jections. A method is proposed for constructing minimum aberration designs using only a partial catalog of some good designs. Minimum aberration designs are constructed for 128 runs up to 64 factors, 256 runs up to 28 factors, and 512, 1024, 2048, and 4096 runs up to 23 or 24 factors. Furthermore, this algorithm is used to completely enumerate all 128-run designs of resolution 4 up to 30 factors, all 256-run designs of resolution 4 up to 17 factors, all 512-run designs of resolution 5, all 1024-run designs of resolution 6, and all 2048- and 4096-run designs of resolution 7.