TOWERS OF GLOBAL FUNCTION-FIELDS WITH ASYMPTOTICALLY MANY RATIONAL PLACES AND AN IMPROVEMENT ON THE GILBERT-VARSHAMOV BOUND

We construct infinite class field towers of global function fields wit h asymptotically many rational places. In this way, we improve on asym ptotic bounds of SERRE, PERRET, SCHOOF, and XING. The results can be i nterpreted equivalently as asymptotic bounds on the number of rational points of smooth algebraic curves over finite fields. As an applicati on, we show an improvement on the Gilbert-Varshamov bound for linear c odes over finite fields of a sufficiently large composite nonsquare or der.