The run matrix can be generated using different strategies.
All strategies sample the parameter region to be approximated as specified
by the user. For instance, a full factorial design is built by
first dividing each parameter interval into 
subintervals where
k is the dependency order of the output on that parameter. The run table
is then formed by taking all possible combinations of parameter values.
The main disadvantage of the full factorial design is the exponential
increase in the number of runs with the number of model parameters.
Different designs are used to limit the number of runs.
Fractional factorial or blocking designs can limit the
number of runs at the expense of cofounding some of the
parameters interaction. For quadratic order models, composite designs
strike a similar balance. They consist of a factorial or
fractional factorial design to estimate first order interaction augmented
with points to estimate the quadratic terms.
A large number of statistically based experimental
designs [68][15] exists. To allow for the generation of
run tables for any of these designs, a Design Of Experiments (DOE) table
specification is implemented. A DOE table is encoded as an 
matrix D, where l is the number of runs and n the number of the parameters
and 
. The run table is generated from the DOE table
using the following transformation:
