Draper and Guttman (1997) shows that for basic 2k−p designs, p≥0, k − p replicates of blocks designs of size two are needed to estimate all the usual (estimable) effects. In this work, we provide an algebraic formal proof for the two-level blocks designs results and present results applicable to the general case; that is, for the case of sk factorial (p=0) or sk−p fractional factorial (p >0) designs in sb blocks, where 0