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Theory of Orthogonal Designs |

A design for *q*-level factors in *q*^{m} runs constructed by the FACTEX procedure
has the following general form. The first *m* factors are taken to
index the runs in the design, with one run for each different
combination of the levels of these factors, where the levels run
from 0 to *q*-1. These factors are called *run-indexing factors*.
For a particular run, the value *F* of any other factor in the design
is derived from the levels *P _{1}*,

where all the arithmetic is performed in the finite field of size *q*.

The linear combination on the right-hand side of the preceding equation is
called a *generalized interaction* between the run-indexing factors.
A generalized interaction is part of the statistical interaction between
the factors with nonzero coefficients in the linear combination. The
factor *F* is said to be *confounded* or *aliased* with
this generalized interaction; two terms are confounded when the levels
they take in the design yield identical partitions of the runs, so that
their effects cannot be distinguished.
The confounding rules characterize the design, and the problem of
constructing the design reduces to finding suitable confounding rules.

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