  We investigate the transport in a two-dimensional (2D) lattice of coupled
Sinai billiards fabricated on the basis of a high-mobility 2D electron gas in
GaAs/AlGaAs heterojunction. For the states with low reduced conductivity g<<1
an anomalously weak temperature dependence of g was found. The large negative
magnetoresistance described by the Lorentz line-shape of the width
corresponding to the half magnetic flux quantum through the area of the
billiard is observed. In going from g>1 to g<<1 it strongly increases. The
Shubnikov-de Haas oscillations and commensurability magnetoresistance peak are
preserved at g<<1. The data suggest that the system studied behaves more like a
metal than an insulator at g<<1 and is not described by the generally accepted
picture of Anderson localization.
