# Lattice Builder

##### Search for good rank-1 lattices

This Web interface allows Lattice Builder users to call the executable program without having to construct the command line explicitly. Refer to the Lattice Builder Manual and to the reference paper for more information.

Enter the construction parameters below, and press the Search button at the bottom. The results will show at the bottom.

### Search Criteria

Lattice Properties

\[ P_n = \left\{ (i \boldsymbol a \bmod n) / n \::\: i = 0, \dots, n - 1 \right\} \qquad (\boldsymbol a \in \mathbb Z^s) \]

Size \(n\)
please enter a valid size, e.g., 127 or 2^10
Lattice Type Embedded
Dimension \(s\)
please enter a positive integer value
Multilevel Filters and Combiner See the reference paper for details.
Normalization
Normalization Type
Minimum Level
Maximum Level
Low-Pass Filter
Low-Pass Threshold
Combiner
Figure of Merit

\[ \left[ \mathcal D_q(P_n) \right]^q = \sum_{\emptyset \neq u \subseteq \{1,\dots,s\}} \gamma_u^q \, \left[\mathcal D_u(P_n)\right]^q \qquad (q > 0) \]

Figure of Merit
Value of \(\alpha\)
Evaluation Method Coordinate-Uniform
Generally faster, but requires \(q=2\).
Norm Type \(q > 0\)
Type `inf` for \(\infty\).
please enter a positive real number or inf
\(q = 2\)
Uncheck Coordinate-Uniform to use \(q \neq 2\).
Weights

\[ \gamma_u^p \qquad (u \subseteq \{1, \dots, s\}) \]

[add]
Weights Power \(p\) Usually \(p=q\) or \(p=1\).
please enter a positive real number
Construction Method
Construction Method
Number \(r\) of Random Samples
please enter a positive integer
Generating Vector \(\boldsymbol a = (a_1, \ldots, a_s)\) [expression] [from results]
Search for Lattices
Waiting for Lattice Builder to respond...

### Search Results

Lattice Size :
Generating Vector :
Merit Value :
CPU Time :
Command Line:
Code to generate points :
[C] [Python] [Matlab] [Plot]
To evaluate another figure of merit with this vector, select the Explicit construction method and click on [from results] above the generating vector input.
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#### Set all weights using an expression

Enter a constant or an expression for the weights, using var as the coordinate index.

Expression =

##### Examples

- 0.1
- 0.1*var^-2
- 1/(1+var^2)
- 0.1^var

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#### Select a new type of weights

- Product Weights
- Order-Dependent Weights
- POD Weights
- Projection-Dependent Weights

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#### Code

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generating vector :1,1 —  number of points :2
Coordinates : Level :