Explicit global function fields over the binary field with many rational places

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1. [1] L. Carlitz, A class of polynomials, Trans. Amer. Math. Soc. 43 (1938), 167-182. Zbl0018.19806
2. [2] A. Garcia and H. Stichtenoth, A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound, Invent. Math. 121 (1995), 211-222. Zbl0822.11078
3. [3] A. Garcia and H. Stichtenoth, On the asymptotic behaviour of some towers of function fields over finite fields, preprint, 1995. Zbl0893.11047
4. [4] D. R. Hayes, Explicit class field theory for rational function fields, Trans. Amer. Math. Soc. 189 (1974), 77-91. Zbl0292.12018
5. [5] Y. Ihara, Some remarks on the number of rational points of algebraic curves over finite fields, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981), 721-724. Zbl0509.14019
6. [6] H. Niederreiter and C. P. Xing, Low-discrepancy sequences obtained from algebraic function fields over finite fields, Acta Arith. 72 (1995), 281-298. Zbl0833.11035
7. [7] H. Niederreiter and C. P. Xing, Low-discrepancy sequences and global function fields with many rational places, Finite Fields Appl., to appear. 
8. [8] H. Niederreiter and C. P. Xing, Quasirandom points and global function fields, in: Finite Fields and Applications, S. D. Cohen and H. Niederreiter (eds.), Cambridge University Press, Cambridge, to appear. Zbl0932.11050
9. [9] M. Perret, Tours ramifiées infinies de corps de classes, J. Number Theory 38 (1991), 300-322. Zbl0741.11044
10. [10] R. Schoof, Algebraic curves over 𝔽₂ with many rational points, J. Number Theory 41 (1992), 6-14. Zbl0762.11026
11. [11] J.-P. Serre, Sur le nombre des points rationnels d'une courbe algébrique sur un corps fini, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), 397-402. Zbl0538.14015
12. [12] J.-P. Serre, Nombres de points des courbes algébriques sur ${}_q$, Sém. Théorie des Nombres 1982-1983, Exp. 22, Univ. de Bordeaux I, Talence, 1983. 
13. [13] J.-P. Serre, Résumé des cours de 1983-1984, Annuaire du Collège de France (1984), 79-83. 
14. [14] J.-P. Serre, Rational Points on Curves over Finite Fields, lecture notes, Harvard University, 1985. 
15. [15] J.-P. Serre, personal communication, August 1995. 
16. [16] H. Stichtenoth, Algebraic Function Fields and Codes, Springer, Berlin, 1993. 
17. [17] M. A. Tsfasman and S. G. Vlădut, Algebraic-Geometric Codes, Kluwer, Dordrecht, 1991. Zbl0727.94007
18. [18] G. van der Geer and M. van der Vlugt, Curves over finite fields of characteristic 2 with many rational points, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), 593-597. Zbl0787.14033
19. [19] E. Weiss, Algebraic Number Theory, McGraw-Hill, New York, 1963. Zbl0115.03601
20. [20] C. P. Xing, Multiple Kummer extension and the number of prime divisors of degree one in function fields, J. Pure Applied Algebra 84 (1993), 85-93. Zbl0776.11068
21. [21] C. P. Xing and H. Niederreiter, A construction of low-discrepancy sequences using global function fields, Acta Arith. 73 (1995), 87-102. Zbl0848.11038

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