Uniform designs based on F-squares. (2016) - Husain, Bushra; Sharma, Sanghmitra
Uniform designs are space filling designs that find applications in many diverse fields. Specifically, uniform designs may be used for computer experiments when the underlying model is too complicated and also for experiments pertaining to industries when the knowledge about the underlying model is vague. Usually, good lattice point sets are used to generate uniform designs. Some practical limitations require the use of F-square based designs. Fang, Shiu and Pan (1999) obtained uniform designs based on cyclic Latin squares. In this paper, we have obtained uniform designs based on cyclic F-squares. These designs have considerably less discrepancies as compared to those obtained by Wang and Fang (1981). The threshold accepting algorithm proposed by Fang, Shiu and Pan (1999) has been employed to obtain the cyclic F-squares with smallest L2 -discrepancy. Numerical comparisons of centred L2 -discrepancy of Latin square based designs with F-uniform designs indicate that the F-uniform designs have lower discrepancy.