How to approximate (with minimal costs) an iterated (multiple) Ito and Stratonovich stochastic integrals (from stochastic Taylor expansions) of high multiplicities (2, 3, 4, 5, ...) when solving numerically Ito SODEs (the case of multidimentional Wiener process)? I am talking about of numerical solution according to the strong criterion. Which basis is optimal in the sense of computing costs when we construct the expansions of iterated stochastic integrals? 1) Piecewise constant basis (method of integral sums by the other words). 2) Classical Fourier basis (trigonometric system of functions). 3) Another Fourier basis (Legendre's polynomials, Haar functions, etc.). 4) Another way?