Best Known (107, 166, s)-Nets in Base 3
(107, 166, 156)-Net over F3 — Constructive and digital
Digital (107, 166, 156)-net over F3, using
- 4 times m-reduction [i] based on digital (107, 170, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 85, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- trace code for nets [i] based on digital (22, 85, 78)-net over F9, using
(107, 166, 224)-Net over F3 — Digital
Digital (107, 166, 224)-net over F3, using
(107, 166, 2996)-Net in Base 3 — Upper bound on s
There is no (107, 166, 2997)-net in base 3, because
- 1 times m-reduction [i] would yield (107, 165, 2997)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 5 320885 825856 366920 884261 732625 582060 083372 259858 681218 398153 355559 155847 870747 > 3165 [i]