Best Known (68, 94, s)-Nets in Base 4
(68, 94, 384)-Net over F4 — Constructive and digital
Digital (68, 94, 384)-net over F4, using
- 41 times duplication [i] based on digital (67, 93, 384)-net over F4, using
- trace code for nets [i] based on digital (5, 31, 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, 31, 128)-net over F64, using
(68, 94, 387)-Net in Base 4 — Constructive
(68, 94, 387)-net in base 4, using
- 41 times duplication [i] based on (67, 93, 387)-net in base 4, using
- trace code for nets [i] based on (5, 31, 129)-net in base 64, using
- 4 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
- 4 times m-reduction [i] based on (5, 35, 129)-net in base 64, using
- trace code for nets [i] based on (5, 31, 129)-net in base 64, using
(68, 94, 635)-Net over F4 — Digital
Digital (68, 94, 635)-net over F4, using
(68, 94, 42612)-Net in Base 4 — Upper bound on s
There is no (68, 94, 42613)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 392 384823 383183 877333 597853 741556 022052 787612 117592 805480 > 494 [i]