AbstractWe prove that each OBDD (ordered binary decision diagram) for the middle bit of n-bit integer multiplication for one of the variable orders which so far achieve the smallest OBDD sizes with respect to asymptotic order of growth, namely the pairwise ascending order x0,y0,…,xn−1,yn−1, requires a size of Ω(2(6/5)n). This is asymptotically optimal due to a bound of the same order by Amano and Maruoka (2007) [1]