Abstract: The minimum aberration criterion is one of the popular criteria for choosing the optimal fractional factorial designs. The paper studies the structure of the 4^1 2^n designs D. For n with 5 N / 16+1 \leq n \leq N / 2, where N is the run size of D, it first obtains the lower bounds of A_30(D) and A_31(D), the key terms which describe the optimality of D, and the structure of D which attains the lower bounds. Then it gives the construction methods of minimum aberration 4^1 2^n designs or weak minimum aberration 4^1 2^n designs.