Best Known (75−48, 75, s)-Nets in Base 128
(75−48, 75, 321)-Net over F128 — Constructive and digital
Digital (27, 75, 321)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 24, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (3, 51, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (0, 24, 129)-net over F128, using
(75−48, 75, 513)-Net over F128 — Digital
Digital (27, 75, 513)-net over F128, using
- t-expansion [i] based on digital (24, 75, 513)-net over F128, using
- net from sequence [i] based on digital (24, 512)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 24 and N(F) ≥ 513, using
- net from sequence [i] based on digital (24, 512)-sequence over F128, using
(75−48, 75, 296874)-Net in Base 128 — Upper bound on s
There is no (27, 75, 296875)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 109 840135 609004 774626 367192 919161 777132 258490 871149 913470 428885 303708 445923 852124 527969 528190 870569 071608 722161 034559 035888 804805 495424 388380 255745 053020 240626 > 12875 [i]