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This paper gives a main effect plus two plan (MEP.2 plan) for 2 m factorials (m>=4) in the same setup as in Mukerjee and Chatterjee (Utilitas Math. 45 (1994) 213) in a smaller number of treatments. For a certain design T 1 , combinatorial properties on a design T 2 are presented so that the design T=T 1 +T 2 is a MEP.2 plan, where ''+'' stands for a union...