Best Known (12, 12+14, s)-Nets in Base 128
(12, 12+14, 408)-Net over F128 — Constructive and digital
Digital (12, 26, 408)-net over F128, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 4, 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 (0, 7, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128 (see above)
- digital (1, 15, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- digital (0, 4, 129)-net over F128, using
(12, 12+14, 515)-Net in Base 128 — Constructive
(12, 26, 515)-net in base 128, using
- (u, u+v)-construction [i] based on
- (1, 8, 257)-net in base 128, using
- base change [i] based on digital (0, 7, 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, 7, 257)-net over F256, using
- (4, 18, 258)-net in base 128, using
- 6 times m-reduction [i] based on (4, 24, 258)-net in base 128, using
- base change [i] based on digital (1, 21, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 21, 258)-net over F256, using
- 6 times m-reduction [i] based on (4, 24, 258)-net in base 128, using
- (1, 8, 257)-net in base 128, using
(12, 12+14, 738)-Net over F128 — Digital
Digital (12, 26, 738)-net over F128, using
(12, 12+14, 1786051)-Net in Base 128 — Upper bound on s
There is no (12, 26, 1786052)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 6 129984 881327 678822 965308 881379 674842 537622 053372 508688 > 12826 [i]