Consequences of the Moosbauer-Poole Algorithms

Moosbauer and Poole have recently shown that the multiplication of two 5 × 5 matrices requires no more than 93 multiplications in the (possibly non-commutative) coefficient ring, and that the multiplication of two 6 × 6 matrices requires no more than 153 multiplications. Taking these multiplication schemes as starting points, we found improved matrix multiplication schemes for various rectangular matrix formats using a flip graph search.