  Frameproof codes have been extensively studied for many years due to their
application in copyright protection and their connection to extremal set
theory. In this paper, we investigate upper bounds on the cardinality of
wide-sense $t$-frameproof codes. For $t=2$, we apply results from Sperner
theory to give a better upper bound, which significantly improves a recent
bound by Zhou and Zhou. For $t\geq 3$, we provide a general upper bound by
establishing a relation between wide-sense frameproof codes and cover-free
families. Finally, when the code length $n$ is at most
$\frac{15+\sqrt{33}}{24}(t-1)^2$, we show that a wide-sense $t$-frameproof code
has at most $n$ codewords, and the unique optimal code consists of all
weight-one codewords. As byproducts, our results improve several best known
results on binary $t$-frameproof codes.
