Best Known (76−46, 76, s)-Nets in Base 128
(76−46, 76, 384)-Net over F128 — Constructive and digital
Digital (30, 76, 384)-net over F128, using
- 2 times m-reduction [i] based on digital (30, 78, 384)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 27, 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, 51, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128 (see above)
- digital (3, 27, 192)-net over F128, using
- (u, u+v)-construction [i] based on
(76−46, 76, 386)-Net in Base 128 — Constructive
(30, 76, 386)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (0, 23, 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, 53, 257)-net in base 128, using
- 3 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
- 3 times m-reduction [i] based on (7, 56, 257)-net in base 128, using
- digital (0, 23, 129)-net over F128, using
(76−46, 76, 609)-Net over F128 — Digital
Digital (30, 76, 609)-net over F128, using
- net from sequence [i] based on digital (30, 608)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 30 and N(F) ≥ 609, using
(76−46, 76, 681710)-Net in Base 128 — Upper bound on s
There is no (30, 76, 681711)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 14059 242556 069375 998328 875729 914490 293132 790026 324607 149947 102974 906929 516328 872712 703505 768678 181315 379853 469951 958052 220258 101728 286865 221595 274880 866608 556848 > 12876 [i]