Best Known (79, 109, s)-Nets in Base 4
(79, 109, 384)-Net over F4 — Constructive and digital
Digital (79, 109, 384)-net over F4, using
- 2 times m-reduction [i] based on digital (79, 111, 384)-net over F4, using
- trace code for nets [i] based on digital (5, 37, 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, 37, 128)-net over F64, using
(79, 109, 387)-Net in Base 4 — Constructive
(79, 109, 387)-net in base 4, using
- 44 times duplication [i] based on (75, 105, 387)-net in base 4, using
- trace code for nets [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
- trace code for nets [i] based on (5, 35, 129)-net in base 64, using
(79, 109, 727)-Net over F4 — Digital
Digital (79, 109, 727)-net over F4, using
(79, 109, 50758)-Net in Base 4 — Upper bound on s
There is no (79, 109, 50759)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 421264 468642 593814 471884 237127 399632 844297 751917 208846 776872 924448 > 4109 [i]