Кубатурные формулы на сфере, инвариантные относительно группы диэдра $\mathrm{D_{2h}}$

An algorithm of searching for the best (in a sense) cubature formulas on a sphere that are invariant under the transformations of dihedral group of rotations with inversion D2h is described. This algorithm is applied to find parameters of all the best cubature formulas of this symmetry group up to the 35th order of accuracy.