Let $\mathbb{B} = \{ 0, 1 \}$ be the D217: Set of boolean numbers.
The set of euclidean boolean numbers with respect to $N \in \{ 1, 2, 3, \ldots \}$ is the D11: Set \begin{equation} \mathbb{B}^N = \prod_{n = 1}^N \mathbb{B} \end{equation}