It is necessary to include centre points as well (in which all factors are at their central values).
In this table, m represents the number of factors which are varied in each of the blocks.
Taking the 9 factor design, deleting one column and any resulting duplicate rows produces an 81 run design for 8 factors, while giving up some "rotatability" (see above).
These designs can be augmented with positive and negative "axial points", as in central composite designs, but, in this case, to estimate univariate cubic and quartic effects, with length α = min(2, (int(1.5 + K/4))1/2), for K factors, roughly to approximate original design points' distances from the centre.
Since each column of the basic design has 50% 0s and 25% each +1s and −1s, multiplying each column, j, by σ(Xj)·21/2 and adding μ(Xj) prior to experimentation, under a general linear model hypothesis, produces a "sample" of output Y with correct first and second moments of Y.