A parallel flats fraction for the 3^ design is defined as union of flats {t│At=c_i (mod 3)}, i=1, 2,…, f and is symbolically written as At=C where A is rank r. The A matrix partitions the effects into u＋1 alias sets where u=(3^n-r―1)/2. For each alias set the f flats produce an ACPM from which a detection matrix is constructed. The set of all possible parallel flats fraction C can be partitioned into equivalence classes. In this paper, we develop some properties of a detection matrix and C.