Theory of Computing
-------------------
Title     : Towards Finding Hay in a Haystack: Explicit Tensors of Border Rank Greater Than $2.02m$ in $\mathbb{C}^m\otimes \mathbb{C}^m\otimes \mathbb{C}^m$
Authors   : Joseph M. Landsberg and Mateusz Michalek
Volume    : 21
Number    : 13
Pages     : 1-17
URL       : https://theoryofcomputing.org/articles/v021a013

Abstract
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We write down an explicit sequence of tensors in C^m * C^m * C^m,
for all $m$ sufficiently large, having border rank at least 2.02m,
overcoming a longstanding barrier. We obtain our lower bounds via
the border substitution method.