  Let $\mathbb{F}$ be an arbitrary field. In this paper, we continue studying
the Terwilliger algebras of association schemes over $\mathbb{F}$ that were
called the Terwilliger $\mathbb{F}$-algebras of association schemes in [8]. We
determine the algebraic structures of the Terwilliger $\mathbb{F}$-algebras of
the association schemes induced from the Cayley tables of elementary abelian
$2$-groups, which provides infinite many examples and counterexamples for the
study of the Terwilliger $\mathbb{F}$-algebras of association schemes.
