Nets, (t, s)-Sequences, and codes

Abstract

Nets and (t, s)-sequences are standard sources of quasirandom points for quasi-Monte Carlo methods. Connections between nets and error-correcting codes have been noticed for a long time, and these links have become even more pronounced with the development of the duality theory for digital nets. In this paper, we further explore these fascinating connections. We present also a recent construction of digital (t, s)-sequences using global function fields and new general constructions of nets and (t, s)-sequences. © 2008 Springer-Verlag Berlin Heidelberg.