Discrete Discrepancy

Given a point set  in the -dimensional unit cube , the star discrepancy is defined as

(1)

where the local discrepancy is defined as

(2)

 is the content of , and  is the class of all discrete subintervals  of  of the form

(3)

with .

REFERENCES:

Niederreiter, H. Random Number Generation and Quasi-Monte Carlo Methods. Philadelphia, PA: SIAM, 1992.