Best Known (107, 170, s)-Nets in Base 3
(107, 170, 156)-Net over F3 — Constructive and digital
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
(107, 170, 202)-Net over F3 — Digital
Digital (107, 170, 202)-net over F3, using
(107, 170, 2447)-Net in Base 3 — Upper bound on s
There is no (107, 170, 2448)-net in base 3, because
- 1 times m-reduction [i] would yield (107, 169, 2448)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 432 432704 364327 679906 102547 021365 062566 974838 356243 059963 197904 904315 754069 029569 > 3169 [i]