  Locally repairable codes have been investigated extensively in recent years
due to practical applications in distributed and cloud storage systems.
However, there are few asymptotical constructions of locally repairable codes
in the literature. In this paper, we provide an explicit asymptotic
construction of locally repairable codes over arbitrary finite fields from
local expansions of functions at a rational place. This construction gives a
Tsfasman-Vladut-Zink type bound for locally repairable codes. Its main
advantage is that there are no constraints on both locality and alphabet size.
Furthermore, we show that the Gilbert-Varshamov type bound on locally
repairable codes over non-prime finite fields can be exceeded for sufficiently
large alphabet size.
