  Frameproof codes are used to fingerprint digital data. It can prevent
copyrighted materials from unauthorized use. In this paper, we study upper and
lower bounds for $w$-frameproof codes of length $N$ over an alphabet of size
$q$. The upper bound is based on a combinatorial approach and the lower bound
is based on a probabilistic construction. Both bounds can improve previous
results when $q$ is small compared to $w$, say $cq\leq w$ for some constant
$c\leq q$. Furthermore, we pay special attention to binary frameproof codes. We
show a binary $w$-frameproof code of length $N$ can not have more than $N$
codewords if $N<\binom{w+1}{2}$.
