Best Known (158, 158+52, s)-Nets in Base 3
(158, 158+52, 328)-Net over F3 — Constructive and digital
Digital (158, 210, 328)-net over F3, using
- 32 times duplication [i] based on digital (156, 208, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 52, 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, 52, 82)-net over F81, using
(158, 158+52, 918)-Net over F3 — Digital
Digital (158, 210, 918)-net over F3, using
(158, 158+52, 37639)-Net in Base 3 — Upper bound on s
There is no (158, 210, 37640)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 15692 634449 532662 466718 166307 973645 921034 561273 827402 309789 264484 158934 140444 461092 497123 183580 850993 > 3210 [i]