The new generator of the random uniformly distributed points

The new scheme for generation of a given number of uniformly distributed points in the hypercube is offered and the main properties of the generator are investigated. In the generator the additional condition is represented: the simply ordered values of each coordinate of all generated points are equidistant from each other. This makes it different from the usual simple generator in which each coordinate of point (vector) is determined by a pseudo random number evenly. The points deduced are more uniformly distributed in space and more full information about the research function is retrieved. Generator was applied in the algorithms of search of global optimization of functions of many continuous variables and in the case of statistical study of these algorithms.