Maximal rank of $4\times 4\times 4$ and $k\times 4\times 3$ tensors over $\mathbb{F}_2$

Abstract

We determine the maximum rank of $4\times 4\times 4$ and $k\times 4\times 3$ multidimensional arrays over the finite field $\mathbb{F}_2$. These results are made possible by a new method of enumerating non-isomorphic tensors.