Modular curves have become popular in coding theory because
certain families over certain finite fields attain the "Vladut-Drinfeld"
bound. In this talk we will begin by discussing the bound of
Vladut-Drinfeld, and then show that the family of modular curves X_0(l)
attain this bound as l goes to infinity. This is well-known. We also
will prove the following more precise fact, whose statement has appeared
in the literature, but never accompanied by a proof: if l is a prime not
equal to p, and g denotes the genus of X_0(l), then the absolute value of
the difference between (p-1)g and the
number of points of X_0(l) over F_{p^2} is at most C_p,
a constant which depends only on p. Our proof of this fact
is based on email discussions with Mike Zieve.