# halton: Compute points in the Halton sequence. In SDraw: Spatially Balanced Sample Draws for Spatial Objects

## Description

Computes points in a multi-dimensional Halton sequence, beginning at specified indices and using specified co-prime bases.

## Usage

 `1` ```halton(n, dim = 1, start = 0, bases = NULL) ```

## Arguments

 `n` A scalar giving the number of values in the Halton points to produce. `dim` A scalar giving the number of dimensions, equal to the number of van der Corput sequences. Technically, `dim==1` produces a van der Corput sequence, `dim>=2` produces Halton sequences. `start` A scalar or a length `dim` vector giving the starting index (location) for each van der Corput sequence. Origin of each sequence is 0. `all(start>=0)` must be true. `bases` A length `dim` vector giving the base to use for each dimension. For a Halton sequence, bases must all be co-prime. No check for common prime factors is performed. If `bases` is `NULL`, the first `dim` primes starting at 2 are used as bases of the Halton sequence. For example, the 4-dimensional Halton sequence would use bases 2, 3, 5, and 7. The 6-dimensional Halton sequence would use 2, 3, 5, 7, 11, and 13. Etc.

## Details

The Halton sequence is a sequence of `dim`-dimensional numbers where each dimension is a (1-dimensional) co-prime van der Corput sequence. Here, all van der Corput sequences use bases that are prime numbers. See references below.

## Value

A matrix of size `n` X `dim`. Each column corresponds to a dimension. Each row is a `dim`-dimensional Halton point.

Trent McDonald

## References

van der Corput sequences are described here: http://en.wikipedia.org/wiki/Van_der_Corput_sequence

Halton sequences are described here: http://en.wikipedia.org/wiki/Halton_sequence

Robertson, B.L., J. A. Brown, T. L. McDonald, and P. Jaksons (2013) BAS: "Balanced Acceptance Sampling of Natural Resources", Biometrics, v69, p. 776-784.

`halton.indices`
 ```1 2``` ```halton(10,2) halton(10,2, floor(runif(2,max=100000))) # A random-start 2-D Halton sequence of length 10 ```