On some special effects in theory on numerical integration and functions recovery

We discuss two questions. First, we consider the existence of close to optimal quadrature formulas with a bad $L^2$-discrepancy of their grids, and the second is the question of how much explicit quadrature formulas are preferable to sorting algorithms. Also, in the model case, we obtaine the solution to the question of approximative possibilities of Smolyak's grid in the problems of recovery of functions.