Best Known (126−36, 126, s)-Nets in Base 4
(126−36, 126, 384)-Net over F4 — Constructive and digital
Digital (90, 126, 384)-net over F4, using
- t-expansion [i] based on digital (89, 126, 384)-net over F4, using
- trace code for nets [i] based on digital (5, 42, 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, 42, 128)-net over F64, using
(126−36, 126, 387)-Net in Base 4 — Constructive
(90, 126, 387)-net in base 4, using
- trace code for nets [i] based on (6, 42, 129)-net in base 64, using
- base change [i] based on digital (0, 36, 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, 36, 129)-net over F128, using
(126−36, 126, 699)-Net over F4 — Digital
Digital (90, 126, 699)-net over F4, using
(126−36, 126, 41235)-Net in Base 4 — Upper bound on s
There is no (90, 126, 41236)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 7237 142051 039802 533953 181460 846849 895888 616326 202368 653293 881627 736523 208915 > 4126 [i]