  We consider symmetric tensors of format: $3 \times 3$ over $\mathbb{F}_p$ for
$p = 2, 3, 5$; $3 \times 3 \times 3$ over $\mathbb{F}_p$ for $p = 2, 3$; and $3
\times 3 \times 3 \times 3$ over $\mathbb{F}_p$ for $p = 2, 3$. In each case we
compute their equivalence classes under the action of the general linear group
$GL_3 (\mathbb{F}_p )$. We use computer algebra to determine the set of tensors
of each symmetric rank, then we compute the orbit of the group action. We
determine the maximum symmetric rank of these tensors and compare it with the
maximum rank.
