The Initialization of Sobol Numbers
To construct a Sobol sequence a set of direction numbers vi,j needs to be selected. There is some freedom in the selection of initial direction numbers. Therefore, it is possible to receive different realisations of the Sobol sequence for selected dimensions. A bad selection of initial numbers can considerably reduce the efficiency of Sobol sequences when used for computation.
Arguably the easiest choice for the initialisation numbers is just to have the l-th leftmost bit set, and all other bits to be zero, i.e. mk,j = 1 for all k and j. This initialisation is usually called unit initialisation. However, such a sequence fails the test for Property A and A’ even for low dimensions and hence this initialisation is bad.
Read more about this topic: Sobol Sequence
Famous quotes containing the word numbers:
“I had but three chairs in my house; one for solitude, two for friendship; three for society. When visitors came in larger and unexpected numbers there was but the third chair for them all, but they generally economized the room by standing up.”
—Henry David Thoreau (1817–1862)