Best Known (57, 57+22, s)-Nets in Base 4
(57, 57+22, 312)-Net over F4 — Constructive and digital
Digital (57, 79, 312)-net over F4, using
- 2 times m-reduction [i] based on digital (57, 81, 312)-net over F4, using
- trace code for nets [i] based on digital (3, 27, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- trace code for nets [i] based on digital (3, 27, 104)-net over F64, using
(57, 57+22, 387)-Net in Base 4 — Constructive
(57, 79, 387)-net in base 4, using
- 41 times duplication [i] based on (56, 78, 387)-net in base 4, using
- trace code for nets [i] based on (4, 26, 129)-net in base 64, using
- 2 times m-reduction [i] based on (4, 28, 129)-net in base 64, using
- base change [i] based on digital (0, 24, 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, 24, 129)-net over F128, using
- 2 times m-reduction [i] based on (4, 28, 129)-net in base 64, using
- trace code for nets [i] based on (4, 26, 129)-net in base 64, using
(57, 57+22, 543)-Net over F4 — Digital
Digital (57, 79, 543)-net over F4, using
(57, 57+22, 34488)-Net in Base 4 — Upper bound on s
There is no (57, 79, 34489)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 365481 082258 219669 448924 391664 436583 091689 389104 > 479 [i]