LatNet Builder is a software library and tool for constructing highly-uniform point sets for quasi Monte-Carlo and randomized quasi Monte-Carlo methods using state-of-the-art techniques.

A previous version of this software, called Lattice Builder, only handled rank-1 lattice rules. Rank-1 polynomial lattices, were later added to Lattice Builder. The current version of the software can also handle digital nets in base 2. All in all, the point set types handled by LatNet Builder include rank-1 (ordinary and polynomial) lattice rules and digital nets in base 2 (Sobol' nets, polynomial lattice rules and nets defined by explicit generating matrices.)

More precisely, LatNet Builder can search for point sets with an arbitrary number of points in any dimension of high quality with respect to various criteria. Such quality criteria are called figures of merit. These figures of merit are parametrized by weights which give different importance to the subprojections of the net. The merits of the subprojections are aggregated using a (weighted) \( \ell_q \) norm with \( q \leq \infty \). LatNet Builder can use various exploration methods to construct the point sets, such as the exhaustive, the random sampling or the component-by-component (CBC) methods.

Additionally LatNet Builder contains more advanced features such as multilevel point sets, extensible point sets, interlaced point sets, normalizations, and filters.

The features of LatNet Builder are summed up in the following table:

Features	Lattice rules		Digital nets
Point set types	rank-1 ordinary lattice rules	rank-1 polynomial lattice rules	Sobol' nets polynomial lattice rules, nets with explicit generating matrices
Figures of merit	Kernel based: \( P_\alpha \), \( R_\alpha \), Spectral test	Kernel based: \( P_\alpha \), \( R \)	Kernel based: \( P_\alpha \), \( R \), Bit equidistribution: t-value, resolution-gap
Weights	projection-dependent, order-dependent, product, product-order-dependent and combined weights
Exploration methods	evaluation, exhaustive, random, full CBC and random CBC
Fast CBC	fast CBC for power of a prime modulus	fast CBC for irreducible modulus	not applicable
Multilevel point sets	embedded lattices		digital sequences
Normalizations and filters	available		not implemented
Interlaced point sets	not applicable	interlaced polynomial lattice rules	interlaced digital nets