Best Known (232−58, 232, s)-Nets in Base 3
(232−58, 232, 328)-Net over F3 — Constructive and digital
Digital (174, 232, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 58, 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
(232−58, 232, 960)-Net over F3 — Digital
Digital (174, 232, 960)-net over F3, using
(232−58, 232, 38259)-Net in Base 3 — Upper bound on s
There is no (174, 232, 38260)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 492 391293 921442 559557 804023 291789 089210 795034 008554 817509 848212 711659 534545 225657 367740 663071 474117 033963 694153 > 3232 [i]