Best Known (86, 166, s)-Nets in Base 8
(86, 166, 208)-Net over F8 — Constructive and digital
Digital (86, 166, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 83, 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
(86, 166, 225)-Net in Base 8 — Constructive
(86, 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
(86, 166, 309)-Net over F8 — Digital
Digital (86, 166, 309)-net over F8, using
(86, 166, 12579)-Net in Base 8 — Upper bound on s
There is no (86, 166, 12580)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 820851 625200 545115 672529 481376 770572 172911 109923 709848 120312 457624 719046 700597 864107 547557 081136 848383 218596 128879 908114 534558 725693 333601 197770 475488 > 8166 [i]