I want to thank Axel Kemper who sent me this beautiful and complete bibliography.
But even more impressive is the following list:
|(1)||3×3 * 3×2||15||Hopcroft|
|(2)||3×3 * 3×2||14||Kemper|
|(4)||3×3 * 3×3||20||Smirnov|
|(5)||2×3 * 3×3||15||Hopcroft|
|(6)||2×2 * 2×2||7||Strassen|
|(8)||3×2 * 2×3||14||Smirnov|
|(9)||2×2 * 2×3||10||Bini|
95 products correspond to a complexity of O(n2,829), which is above the Strassen complexity of O(n2,80735). To stay below Strassen, a solution for 5x5x5 must not have more than 91 products. Where, the above algorithms have a matrix format:
or if you are inclined to a “pseudo-code” version a much longer list is available here
All algorithms are verified.