Best Known (78−22, 78, s)-Nets in Base 4
(78−22, 78, 312)-Net over F4 — Constructive and digital
Digital (56, 78, 312)-net over F4, using
- t-expansion [i] based on digital (55, 78, 312)-net over F4, using
- trace code for nets [i] based on digital (3, 26, 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, 26, 104)-net over F64, using
(78−22, 78, 387)-Net in Base 4 — Constructive
(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
(78−22, 78, 509)-Net over F4 — Digital
Digital (56, 78, 509)-net over F4, using
(78−22, 78, 30403)-Net in Base 4 — Upper bound on s
There is no (56, 78, 30404)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 91364 493997 614574 900355 962564 691759 291024 430328 > 478 [i]