Best Known (139, 139+46, s)-Nets in Base 3
(139, 139+46, 328)-Net over F3 — Constructive and digital
Digital (139, 185, 328)-net over F3, using
- 31 times duplication [i] based on digital (138, 184, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 46, 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, 46, 82)-net over F81, using
(139, 139+46, 815)-Net over F3 — Digital
Digital (139, 185, 815)-net over F3, using
(139, 139+46, 32421)-Net in Base 3 — Upper bound on s
There is no (139, 185, 32422)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 18511 364546 633142 148194 615348 926106 267164 788009 556409 991639 562393 530039 748673 800921 824761 > 3185 [i]