This paper considers the construction of 2n-k: 2p designs with weak minimum aberra- tion,where a 2n-k: 2p design denotes a blocked two-level design with n treatment factors,2p blocks,and N = 2n-k runs.We first obtain the mimmum value of A2.1,the number of two-factor interac- tions which are aliased with the block effects.We next propose a method to construct the blocked two-level designs such that A3.0 and A2,1 are minimized simultaneously when n≤N 2 - 2p-1,where A3.0 is the number of defining words of length 3 involving only the treatment factors.When N/2 - 2p-1 < n≤N/2,A3,0 and A2,1 can not be minimized simultaneously.Another construction method is then suggested to minimize A3,0 and A2,1 sequentially.The designs constructed by both methods are weak minimum aberrations with respect to some existing combined wordlength pat- terns.The constructed designs with 128 runs and more than 128 runs are new and supplement the existing tables in the literature.