  We study the dispersion of digital $(0,m,2)$-nets; i.e. the size of the
largest axes-parallel box within such point sets. Digital nets are an important
class of low-discrepancy point sets. We prove tight lower and upper bounds for
certain subclasses of digital nets where the generating matrices are of
triangular form and compute the dispersion of special nets such as the
Hammersley point set exactly.
