Why does my quasi-random numbers, generated with the HALTONSET, not fill each of the dimensions?

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I am generating some quasi-random numbers using the HALTONSET class. However, the points returned are not always uniformly distributed over each of the dimensions.
For example, the following code generates quasi-random points that should fill the 30 dimensional unit hypercube:
p = haltonset(30,'Skip',1e7,'Leap',1e2);
X = net(p,1000);
figure, boxplot(X)
However, you can see that values for dimension 26 are not evenly distributed over the unit interval.

Accepted Answer

MathWorks Support Team
MathWorks Support Team on 18 Oct 2013
This change has been incorporated into the documentation in Release 2010a (R2010a). For previous releases, read below for any additional information:
Many Leap values create sequences that fail to touch on large sub-hyper-rectangles of the unit hypercube, and so fail to be a uniform quasi-random point set.
A known rule for choosing Leap values for Halton sets is to set it to (P-1) where P is a prime number that has not been used to generate one of the dimensions, i.e. for a k-dimensional point set P would be the (k+1)th or greater prime.
So in this 30 dimensional example, a suitable Leap value would be the 31st prime - 1, i.e., 127-1 = 126:
p = haltonset(30,'Skip',1e7,'Leap',126);
X = net(p,1000);

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