 Fractional factorial design

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.

Fractional factorial design is a type of experimental design used in statistics and research to study the effects of multiple factors on a response variable while using a reduced number of experimental runs. This design is particularly useful when time, resources, or costs are limited, allowing researchers to efficiently assess the influence of several factors without conducting a full factorial experiment, which could involve an unmanageable number of trials.