Best Known (242−60, 242, s)-Nets in Base 3
(242−60, 242, 328)-Net over F3 — Constructive and digital
Digital (182, 242, 328)-net over F3, using
- 32 times duplication [i] based on digital (180, 240, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 60, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 60, 82)-net over F81, using
(242−60, 242, 1028)-Net over F3 — Digital
Digital (182, 242, 1028)-net over F3, using
(242−60, 242, 42484)-Net in Base 3 — Upper bound on s
There is no (182, 242, 42485)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 29 063602 792605 796177 927108 820820 913986 157192 792690 043503 569693 273060 451377 839625 853633 698776 351373 563017 174852 671745 > 3242 [i]