Best Known (128, 128+42, s)-Nets in Base 3
(128, 128+42, 328)-Net over F3 — Constructive and digital
Digital (128, 170, 328)-net over F3, using
- 32 times duplication [i] based on digital (126, 168, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 42, 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, 42, 82)-net over F81, using
(128, 128+42, 783)-Net over F3 — Digital
Digital (128, 170, 783)-net over F3, using
(128, 128+42, 31593)-Net in Base 3 — Upper bound on s
There is no (128, 170, 31594)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1290 913264 086461 847802 595223 287351 964036 310965 963697 424623 622429 980802 169871 839117 > 3170 [i]