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For tensors in $\mathbb{C}^d \otimes \mathbb{C}^d \otimes \mathbb{C}^d$,Landsberg provides non-trivial equations for tensors of border rank $2d-3$ for$d$ even and $2d-5$ for $d$ odd were found by Landsberg. In previous work, weobserve that Landsberg's method can be interpreted in the language of tensorblow-ups of matrix spaces, and using concavity of blow-ups we improve the casefor odd $d$ from $2d-5$ to $2d-4$. The purpose of this paper is to show thatthe aforementioned results extend to tensors in $K^d \otimes K^d \otimes K^d$for any field $K$.

Explicit tensors of border rank at least $2d-2$ in $K^d \otimes K^d \otimes K^d$ in arbitrary characteristic