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A subspace code of size $333$ in the setting of a binary $q$-analog of the Fano plane
Daniel Heinlein, Michael Kiermaier, Sascha Kurz, Alfred Wasserma · 2017-08-21 · via cs.IT updates on arXiv.org

We show that there is a binary subspace code of constant dimension 3 in ambient dimension 7, having minimum distance 4 and cardinality 333, i.e., $333 \le A_2(7,4;3)$, which improves the previous best known lower bound of 329. Moreover, if a code with these parameters has at least 333 elements, its automorphism group is in one of $31$ conjugacy classes. This is achieved by a more general technique for an exhaustive search in a finite group that does not depend on the enumeration of all subgroups.

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