Best Known (70, 97, s)-Nets in Base 4
(70, 97, 384)-Net over F4 — Constructive and digital
Digital (70, 97, 384)-net over F4, using
- 41 times duplication [i] based on digital (69, 96, 384)-net over F4, using
- trace code for nets [i] based on digital (5, 32, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- trace code for nets [i] based on digital (5, 32, 128)-net over F64, using
(70, 97, 387)-Net in Base 4 — Constructive
(70, 97, 387)-net in base 4, using
- 41 times duplication [i] based on (69, 96, 387)-net in base 4, using
- trace code for nets [i] based on (5, 32, 129)-net in base 64, using
- 3 times m-reduction [i] based on (5, 35, 129)-net in base 64, using
- base change [i] based on digital (0, 30, 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
- base change [i] based on digital (0, 30, 129)-net over F128, using
- 3 times m-reduction [i] based on (5, 35, 129)-net in base 64, using
- trace code for nets [i] based on (5, 32, 129)-net in base 64, using
(70, 97, 633)-Net over F4 — Digital
Digital (70, 97, 633)-net over F4, using
(70, 97, 52745)-Net in Base 4 — Upper bound on s
There is no (70, 97, 52746)-net in base 4, because
- 1 times m-reduction [i] would yield (70, 96, 52746)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 6278 642530 143053 989034 700454 796486 772056 905339 705723 917184 > 496 [i]