Latin HyperCube

A square grid containing sample positions is a Latin square if, and only if, there is only one sample in each row and each column. A Latin HyperCube DOE, categorized as a space filling DOE, is the generalization of this concept to an arbitrary number of dimensions.

When sampling a design space of N variables, the range of each variable is divided into M equally probable intervals. M sample points are then placed to satisfy the Latin HyperCube requirements. As a result, all experiments have unique levels for each input variable and the number of sample points, M, is not a function of the number of input variables.

Figure 1.

Figure 2. . Latin HyperCube (left) and Hammersley (right) for 100 runs.

Usability Characteristics

  • To get a good quality fitting function, a minimum number of runs should be evaluated. (N+1)(N+2)/2 runs are needed to fit a second order polynomial, assuming that most output responses are close to a second order polynomial within the commonly used input variable ranges of -+10%. An additional number of runs equal to 10% is recommended to provide redundancy, which results in more reliable post-processing. As a result, this equation is recommend to calculate the number of runs needed or a minimum of 1.1*(N+1)(N+2)/2 runs.
  • The structure of a Latin HyperCube run matrix ensures that the runs are orthogonal. Orthogonality is desirable because it is less likely to result in singularities when creating Least Squares Regression fits.
  • Any data in the inclusion matrix is combined with the run data for post-processing. Any run matrix point which is already part of the inclusion data will not be rerun.


In the Specifications step, Settings tab, change method settings.
Parameter Default Range Description
Number of Runs 1.1 ( N + 1 ) ( N + 2 ) 2 > 0 integer Number of new designs to be evaluated.
Random Seed 1 Integer

0 to 10000

Controlling repeatability of runs depending on the way the sequence of random numbers is generated.
Random (non-repeatable).
Triggers a new sequence of pseudo-random numbers, repeatable if the same number is specified.
Use Inclusion Matrix Off Off or On Concatenation without duplication between the inclusion and the generated run matrix.