What does Minitab store in the DOE design matrix for a factorial design?

Minitab uses the design matrix as the x-values in regression analysis to fit models specified in Design of Experiments (DOE). The design matrix contains n rows, where n is the number of observations, and one or more columns for each term in the model. The first column is usually the constant, which contains 1s. The columns for the terms in the model are stored in the following order:
Each covariate has one column in the design matrix.
For each factor, the number of columns equals its degrees of freedom. For example, a three-level factor has two degrees of freedom, and thus Minitab stores two columns for that factor.
For interactions, the number of columns Minitab stores equals the number of degrees of freedom for the interaction term, or the product of the number of columns for the involved factors. For a 2-way interaction with 2-level factors, Minitab stores 1 column.

In DOE, if the design includes k blocks, Minitab stores k - 1 columns for the blocks.

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