Best Known (73−44, 73, s)-Nets in Base 128
(73−44, 73, 384)-Net over F128 — Constructive and digital
Digital (29, 73, 384)-net over F128, using
- 2 times m-reduction [i] based on digital (29, 75, 384)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 26, 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 (3, 49, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128 (see above)
- digital (3, 26, 192)-net over F128, using
- (u, u+v)-construction [i] based on
(73−44, 73, 386)-Net in Base 128 — Constructive
(29, 73, 386)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (0, 22, 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
- (7, 51, 257)-net in base 128, using
- 5 times m-reduction [i] based on (7, 56, 257)-net in base 128, using
- base change [i] based on digital (0, 49, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 49, 257)-net over F256, using
- 5 times m-reduction [i] based on (7, 56, 257)-net in base 128, using
- digital (0, 22, 129)-net over F128, using
(73−44, 73, 577)-Net over F128 — Digital
Digital (29, 73, 577)-net over F128, using
- t-expansion [i] based on digital (28, 73, 577)-net over F128, using
- net from sequence [i] based on digital (28, 576)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 28 and N(F) ≥ 577, using
- net from sequence [i] based on digital (28, 576)-sequence over F128, using
(73−44, 73, 700081)-Net in Base 128 — Upper bound on s
There is no (29, 73, 700082)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 6704 045996 005119 787413 740847 425336 486193 221674 875830 687357 991665 881067 982659 376163 523086 067657 753544 482706 869745 212569 864241 081476 087076 714509 168115 933712 > 12873 [i]