Best Known (178−40, 178, s)-Nets in Base 3
(178−40, 178, 600)-Net over F3 — Constructive and digital
Digital (138, 178, 600)-net over F3, using
- 32 times duplication [i] based on digital (136, 176, 600)-net over F3, using
- trace code for nets [i] based on digital (4, 44, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- trace code for nets [i] based on digital (4, 44, 150)-net over F81, using
(178−40, 178, 1178)-Net over F3 — Digital
Digital (138, 178, 1178)-net over F3, using
(178−40, 178, 73204)-Net in Base 3 — Upper bound on s
There is no (138, 178, 73205)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 8 464539 499356 286621 665520 697078 563599 383980 572897 978571 466718 327902 914498 786022 518161 > 3178 [i]