Most figures of merit implemented in LatNet Builder can be parametrized by weights.

Weights are used to put more importance on specific projections of the point set. Various types of weights have been proposed. LatNet Builder implements the following types of weights:

projection-dependent weights:
With projection-dependent weights, the weight associated to the projection onto the coordinates in \(\mathfrak u\) can be set to any non-negative constant \(\gamma_{\mathfrak u}\).
order-dependent weights:
With order-dependent weights, the weight associated to the projection onto the coordinates in \(\mathfrak u\) is
\[ \gamma_{\mathfrak u} = \Gamma_{|\mathfrak u|}. \]
product weights:
With product weights, the weight associated to the projection onto the coordinates in \(\mathfrak u\) is
\[ \gamma_{\mathfrak u} = \prod_{j \in \mathfrak u} \gamma_j. \]
product and order dependent weights:
With product and order-dependent (POD) weights, the weight associated to the projection onto the coordinates in \(\mathfrak u\) is
\[ \gamma_{\mathfrak u} = \Gamma_{|\mathfrak u|} \prod_{j \in \mathfrak u} \gamma_j. \]
combined weights:
With combined weights, the weight associated to the projection onto the coordinates in \(\mathfrak u\) is a sum of weights of different types.

All the types of weights are special cases of projection-dependent weights. They could have been treated as such but for efficiency purposes in coordinate-evaluation algorithms, they are treated separately.