TY - JOUR
T1 - The existence of good extensible rank-1 lattices
AU - Hickernell, Fred J.
AU - Niederreiter, Harald
N1 - Funding Information:
This work was partially supported by a Hong Kong Research Grants Council Grant HKBU/2030/99P.
PY - 2003/6
Y1 - 2003/6
N2 - Extensible integration lattices have the attractive property that the number of points in the node set may be increased while retaining the existing points. It is shown here that there exist generating vectors, h, for extensible rank-1 lattices such that for n = b, b2, ... points and dimensions s = 1, 2, ... the figures of merit Rα, Pα, and discrepancy are all small. The upper bounds obtained on these figures of merit for extensible lattices are some power of log n worse than the best upper bounds for lattices where h is allowed to vary with n and s.
AB - Extensible integration lattices have the attractive property that the number of points in the node set may be increased while retaining the existing points. It is shown here that there exist generating vectors, h, for extensible rank-1 lattices such that for n = b, b2, ... points and dimensions s = 1, 2, ... the figures of merit Rα, Pα, and discrepancy are all small. The upper bounds obtained on these figures of merit for extensible lattices are some power of log n worse than the best upper bounds for lattices where h is allowed to vary with n and s.
KW - Discrepancy
KW - Extensible lattices
KW - Figures of merit
KW - Lattice rules
KW - Quasi-Monte Carlo integration
UR - http://www.scopus.com/inward/record.url?scp=0037648331&partnerID=8YFLogxK
U2 - 10.1016/S0885-064X(02)00026-2
DO - 10.1016/S0885-064X(02)00026-2
M3 - Journal article
AN - SCOPUS:0037648331
SN - 0885-064X
VL - 19
SP - 286
EP - 300
JO - Journal of Complexity
JF - Journal of Complexity
IS - 3
ER -