where disc ⁡ ( z ) = 1 N ∑ i = 1 N ∏ j = 1 d 1 [ 0 , z j ) ( x i , j ) − ∏ j = 1 d z i {\displaystyle \operatorname {disc} (z)={\frac {1}{N}}\sum _{i=1}^{N}\prod _{j=1}^{d}1_{[0,z_{j})}(x_{i,j})-\prod _{j=1}^{d}z_{i}} is the discrepancy function.