This paper presents new results for fast matrix multiplication in small formats obtained by combining the meta flip graph framework with the serendipitous product construction. The framework has been extended to support all 680 rectangular formats with dimensions up to $16 \times 16 \times 16$. Compared to the previous state of the art, ranks are improved for 207 formats. For 84 formats, ternary schemes are found where previously only integer or rational coefficients were known. Additionally, 23 new schemes with asymptotic exponent $ω< \log_2 7$ are discovered, bringing the total number of such schemes to 52. The overall distribution of coefficient types across all investigated formats is 375 ternary, 18 integer, and 287 rational. All code and discovered schemes are available as open source.

翻译：本文通过结合元翻转图框架与偶然乘积构造，给出了小规模快速矩阵乘法的新结果。该框架已扩展至支持所有680种矩形格式，其维度上限为$16 \times 16 \times 16$。与先前最优结果相比，207种格式的秩得到了改进。针对84种格式，发现了此前仅已知整数或有理系数的三元方案。此外，新发现了23个渐近指数$ω< \log_2 7$的方案，使此类方案总数增至52个。所有研究格式的系数类型总体分布为：375个三元系数、18个整数系数和287个有理系数。所有代码及发现方案均以开源形式提供。