Efficiency of numerical integration algorithms related to divisor theory in cyclotomic fields

For function classes with dominant mixed derivative and bounded mixed difference in the metric of $L^q$ ($1<q\le2$), quadrature formulas are constructed so that the following properties are achieved simultaneously: the grid is simple, the algorithm is efficient and close to the optimal algorithm for constructing the grid, and the order of the error on the power scale cannot be further improved. The case $q=2$ was studied earlier.