DOCUMENTA MATHEMATICA, Extra Volume ICM III (1998), 377-386

Harald Niederreiter

Title: Nets, $(t,s)$-Sequences, and Algebraic Curves over Finite Fields with Many Rational Points

The current status of the theory of $(t,m,s)$-nets and $(t,s)$-sequences is presented in a brief form, with some emphasis on the connections with algebraic geometry. Closely related work on constructions of algebraic curves over finite fields with many rational points and on improving the Gilbert-Varshamov bound in algebraic coding theory is discussed as well.

1991 Mathematics Subject Classification: 05B15, 11G20, 11K38, 11R58, 11T71, 14G15, 14H05, 94B27, 94B65.

Keywords and Phrases: quasirandom points, orthogonal arrays, algebraic curves over finite fields, rational points, algebraic-geometry codes, Gilbert-Varshamov bound.

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