Best Known (82−68, 82, s)-Nets in Base 81
(82−68, 82, 224)-Net over F81 — Constructive and digital
Digital (14, 82, 224)-net over F81, using
- t-expansion [i] based on digital (13, 82, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
(82−68, 82, 298)-Net over F81 — Digital
Digital (14, 82, 298)-net over F81, using
- t-expansion [i] based on digital (12, 82, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
(82−68, 82, 6762)-Net in Base 81 — Upper bound on s
There is no (14, 82, 6763)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 3 137064 637741 158865 628387 715975 779953 348452 306233 470177 148087 378105 595770 812572 331048 203848 919761 611809 801292 570961 822706 734351 742667 393443 315377 805682 561761 > 8182 [i]