# Documentation

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# haltonset

Class: haltonset

Construct Halton quasi-random point set

## Syntax

```p = haltonset(d) p = haltonset(d,prop1,val1,prop2,val2,...) ```

## Description

`p = haltonset(d)` constructs a `d`-dimensional point set `p` of the `haltonset` class, with default property settings.

`p = haltonset(d,prop1,val1,prop2,val2,...)` specifies property name/value pairs used to construct `p`.

The object `p` returned by `haltonset` encapsulates properties of a specified quasi-random sequence. The point set is finite, with a length determined by the `Skip` and `Leap` properties and by limits on the size of point set indices (maximum value of 253). Values of the point set are not generated and stored in memory until you access `p` using `net` or parenthesis indexing.

## Examples

Generate a 3-D Halton point set, skip the first 1000 values, and then retain every 101st point:

```p = haltonset(3,'Skip',1e3,'Leap',1e2) p = Halton point set in 3 dimensions (8.918019e+013 points) Properties: Skip : 1000 Leap : 100 ScrambleMethod : none```

Use `scramble` to apply reverse-radix scrambling:

```p = scramble(p,'RR2') p = Halton point set in 3 dimensions (8.918019e+013 points) Properties: Skip : 1000 Leap : 100 ScrambleMethod : RR2```

Use `net` to generate the first four points:

```X0 = net(p,4) X0 = 0.0928 0.6950 0.0029 0.6958 0.2958 0.8269 0.3013 0.6497 0.4141 0.9087 0.7883 0.2166```

Use parenthesis indexing to generate every third point, up to the 11th point:

```X = p(1:3:11,:) X = 0.0928 0.6950 0.0029 0.9087 0.7883 0.2166 0.3843 0.9840 0.9878 0.6831 0.7357 0.7923```

## References

[1] Kocis, L., and W. J. Whiten. “Computational Investigations of Low-Discrepancy Sequences.” ACM Transactions on Mathematical Software. Vol. 23, No. 2, 1997, pp. 266–294.