Journal article

Publication year: 2006

Pages: 859-878

Journal: Mathematics of Computation

Volume number: 75

Issue number: 254

ISSN: 0025-5718

DOI Link: https://doi.org/10.1090/S0025-5718-05-01806-5

Publisher: American Mathematical Society

Abstract: 
New lower bounds for three- and four-level designs under the centered L-2-discrepancy are provided. We describe necessary conditions for the existence of a uniform design meeting these lower bounds. We consider several modi. cations of two stochastic optimization algorithms for the problem of finding uniform or close to uniform designs under the centered L-2-discrepancy. Besides the threshold accepting algorithm, we introduce an algorithm named balance-pursuit heuristic. This algorithm uses some combinatorial properties of inner structures required for a uniform design. Using the best specifications of these algorithms we obtain many designs whose discrepancy is lower than those obtained in previous works, as well as many new low-discrepancy designs with fairly large scale. Moreover, some of these designs meet the lower bound, i.e., are uniform designs.

Harvard Citation style: Fang, K., Maringer, D., Tang, Y. and Winker, P. (2006) Lower bounds and stochastic optimization algorithms for uniform designs with three or four levels, Mathematics of Computation, 75(254), pp. 859-878. https://doi.org/10.1090/S0025-5718-05-01806-5

APA Citation style: Fang, K., Maringer, D., Tang, Y., & Winker, P. (2006). Lower bounds and stochastic optimization algorithms for uniform designs with three or four levels. Mathematics of Computation. 75(254), 859-878. https://doi.org/10.1090/S0025-5718-05-01806-5