Geodesic
Non-existence of a short algorithm for multiplication of $3\times 3$ matrices whose group is $S_4\times S_3$,~II
Trudy Instituta matematiki, Tome 31 (2023) no. 1, pp. 101-111

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It is proved that there is no algorithm for multiplication of $3\times 3$ matrices of multiplicative length $\leqslant 23$ that is invariant under a certain group isomorphic to $S_4\times S_3$. The proof uses description of the orbits of this group on decomposable tensors in the tensor cube $(M_3(\mathbb{C}))^{\otimes 3}$ which was obtained earlier. 
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V. P. Burichenko. Non-existence of a short algorithm for multiplication of $3\times 3$ matrices whose group is $S_4\times S_3$,~II. Trudy Instituta matematiki, Tome 31 (2023) no. 1, pp. 101-111. http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a11/