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Zhang,Li,Zhao and Ai (2008) introduced a new pattern,called aliased effect number pattern (AENP),for classifying regular factorial designs.Based on the AENP,they proposed a general minimum lower order confounding (GMC) criterion for the selection of designs,and the optimal design selected by the GMC criterion is called a GMC design.Subsequently,all the GMC 2n-m designs with N/4+1 ≤ n ≤ N- 1 have been obtained (Li,Zhao and Zhang (2010),Zhang and Cheng (2010),and Cheng and Zhang (2010)),where N = 2n-m is the number of runs and n is the number of factors.Aiming for an efficient implementation of GMC designs in practice,we introduce here a new notion,called Factor-AENP (F-AENP),for ranking the columns of a regular design.We then find all the best F-AENP columns for any GMC 2n- m design with 5N/16 ≤ n ≤ N - 1.The relationship between the F-AENP and AENP of a design is also given.In order to facilitate practical use of the established results,the F-AENPs of the GMC 2n-m designs for 5N/16 + 1 ≤ n ≤ N - 1 with N = 16.32 and 64 are tabulated.