= Fractional factorial design
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A fractional <factorial design> uses a selected subset of the full factor-level combinations. In a regular two-level fraction, encode levels by signs and impose $k$ independent equations $\prod_{j\in G_i}x_j=s_i$. Independence of the generator incidence vectors over $\mathbb F_2$ leaves $2^{m-k}$ runs. Reduced run count creates <aliasing in a fractional factorial design>, which must be evaluated against the effects scientifically required.
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