Best Known (166−82, 166, s)-Nets in Base 8
(166−82, 166, 160)-Net over F8 — Constructive and digital
Digital (84, 166, 160)-net over F8, using
- trace code for nets [i] based on digital (1, 83, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
(166−82, 166, 225)-Net in Base 8 — Constructive
(84, 166, 225)-net in base 8, using
- t-expansion [i] based on (83, 166, 225)-net in base 8, using
- 6 times m-reduction [i] based on (83, 172, 225)-net in base 8, using
- base change [i] based on digital (40, 129, 225)-net over F16, using
- net from sequence [i] based on digital (40, 224)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225, using
- net from sequence [i] based on digital (40, 224)-sequence over F16, using
- base change [i] based on digital (40, 129, 225)-net over F16, using
- 6 times m-reduction [i] based on (83, 172, 225)-net in base 8, using
(166−82, 166, 279)-Net over F8 — Digital
Digital (84, 166, 279)-net over F8, using
(166−82, 166, 10426)-Net in Base 8 — Upper bound on s
There is no (84, 166, 10427)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 818828 859709 452014 298538 929096 034837 440817 210919 749955 686514 160940 653864 198903 786515 031681 416579 043121 754516 571835 323967 557367 491008 786715 638280 780630 > 8166 [i]