[On the wikipedia article](https://en.wikipedia.org/wiki/Hadamard_matrix) about Hadamard Matrix it says that "The smallest order that cannot be constructed by a combination of Sylvester's and Paley's methods is $92$"

But it also says that a new Hadamard matrix of size $nm$ can be created using Hadamard matrices of sizes $n$ and $m$.

Why isn't $23$ ($92=2 \times 2 \times 23$) the smallest size which cannot be created this way?