Rational Points on Curves Over Finite Fields: Theory and Applications

By H. Niederreiter, Chaoping Xing. 2001

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Handbook of Finite Fields (2013, methodology): “4 Remark (Class field towers) [6, 31, 35, 37] Starting with any function field F0 of genus g0 ≥ 2 and a set S0 of rational places of F0, one defines inductively the field Fn+1 to be the maximal abelian unramified extension of Fn in which all places of Sn split completely, and Sn+1 to be the set of a”
Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration (2010, background): “Further information can also be found in the books of Weiss [262] or of Niederreiter & Xing [193].”
An explicit tower of function fields over cubic finite fields and Zink’s lower bound (2005, methodology): “in coding theory and cryptography (see [13] and [16]), it is therefore desirable to construct sequences of function fields ðFnÞnf1 over Fl explicitly such that lim n!y NðFnÞ=gðFnÞ is positive (or even better, a large number).”