Currently, the algorithm with the best computational complexity is a 2019 algorithm of David Harvey and Joris van der Hoeven, which uses the strategies of using number-theoretic transforms introduced with the Schönhage–Strassen algorithm to multiply integers using only operations. This is conjectured to be the best possible algorithm, but lower bounds of are not known.
Currently, the algorithm with the best computational complexity is a 2019 algorithm of David Harvey and Joris van der Hoeven, which uses the strategies of using number-theoretic transforms introduced with. the Schönhage–Str.assen algorithm to :multiply integers using only operations. This is conjectured to be the best possible algorithm, but lower bounds of are not known.