Best Known (120−34, 120, s)-Nets in Base 4
(120−34, 120, 384)-Net over F4 — Constructive and digital
Digital (86, 120, 384)-net over F4, using
- t-expansion [i] based on digital (85, 120, 384)-net over F4, using
- trace code for nets [i] based on digital (5, 40, 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, 40, 128)-net over F64, using
(120−34, 120, 387)-Net in Base 4 — Constructive
(86, 120, 387)-net in base 4, using
- trace code for nets [i] based on (6, 40, 129)-net in base 64, using
- 2 times m-reduction [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
- 2 times m-reduction [i] based on (6, 42, 129)-net in base 64, using
(120−34, 120, 695)-Net over F4 — Digital
Digital (86, 120, 695)-net over F4, using
(120−34, 120, 42512)-Net in Base 4 — Upper bound on s
There is no (86, 120, 42513)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1 766995 127718 684864 189115 162904 142988 393230 898860 715673 101089 028772 008900 > 4120 [i]