# Lattice Builder

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

WARNING: This demo version can only handle small searches.

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

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

please enter a valid size, e.g., 127 or 2^10
please enter a positive integer value
Multilevel Filters and Combiner See the reference paper for details.

Figure of Merit

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

Generally faster, but requires $$q=2$$.
Type inf for $$\infty$$.
please enter a positive real number or inf
$$q = 2$$
Uncheck Coordinate-Uniform to use $$q \neq 2$$.
Weights

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

Usually $$p=q$$ or $$p=1$$.
please enter a positive real number
Construction Method
Search for Lattices
Waiting for Lattice Builder to respond...

### Search Results

Lattice Size :
Generating Vector :
Merit Value :
CPU Time :
Code to generate points :
To evaluate another figure of merit with this vector, select the Explicit construction method and click on [from results] above the generating vector input.

#### Set all weights using an expression

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

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

#### Code

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