By Harald Niederreiter

Ever because the seminal paintings of Goppa on algebraic-geometry codes, rational issues on algebraic curves over finite fields were a big study subject for algebraic geometers and coding theorists. the point of interest during this software of algebraic geometry to coding conception is on algebraic curves over finite fields with many rational issues (relative to the genus). lately, the authors stumbled on one other very important program of such curves, particularly to the development of low-discrepancy sequences. those sequences are wanted for numerical tools in components as diversified as computational physics and mathematical finance. This has given extra impetus to the speculation of, and the hunt for, algebraic curves over finite fields with many rational issues. This publication goals to sum up the theoretical paintings on algebraic curves over finite fields with many rational issues and to debate the functions of such curves to algebraic coding conception and the development of low-discrepancy sequences.