Exercise 4.2.5

V. Pan has discovered a way of multiplying $68 \times 68$ matrices using $132,464$ multiplications, a way of multiplying $70 \times 70$ matrices using $143,640$ multiplications, and a way of multiplying $72 \times 72$ matrices using $155,424$ multiplications. Which method yields the best asymptotic running time when used in a divide-and-conquer matrix-multiplication algorithm? How does it compare to Strassen's algorithm?

Using what we know from the last exercise, we need to pick the smalles of the following:

$$ \log_{68} 132464 \approx 2.795128 \\ \log_{70} 143640 \approx 2.795122 \\ \log_{72} 155424 \approx 2.795147 $$

The fastest one asymptotically is $70 \times 70$ using $143,640$.