Constructions of digital nets using global function fields

Constructions of Digital Nets Using Global Function Fields

A construction of low-discrepancy sequences using global function fields

1. Introduction. The idea of using global function fields for the construction of s-dimensional low-discrepancy sequences was first sketched by Niederreiter [9, Section 5], [10, Section 5], and the details were worked out in an improved form by Niederreiter and Xing [11]. In the method of [11] one chooses a suitable global function field which contains s elements satisfying special properties. ...

Witt Equivalence of Function Fields over Global Fields

Witt equivalent fields can be understood to be fields having the same symmetric bilinear form theory. Witt equivalence of finite fields, local fields and global fields is well understood. Witt equivalence of function fields of curves defined over archimedean local fields is also well understood. In the present paper, Witt equivalence of general function fields over global fields is studied. It ...

Everywhere Ramified Towers of Global Function Fields

We construct a tower of function fields F0 ⊂ F1 ⊂ . . . over a finite field such that every place of every Fi ramifies in the tower and lim genus(Fi)/[Fi : F0] <∞. We also construct a tower in which every place ramifies and limNFi/[Fi : F0] > 0, where NFi is the number of degree-1 places of Fi. These towers answer questions posed by Stichtenoth at Fq7.

Global Ideal Theory of Meromorphic Function Fields

It is shown that the ideal theories of the fields of all meromorphic functions on any two noncompact Riemann surfaces are isomorphic. Further, various new representation and factorization theorems are proved. Introduction. Throughout this paper let X and Y denote noncompact (connected) Riemann surfaces. Let A(X) (or A for short), denote the ring of all analytic functions on X, and let F(X) (or ...