Best Known (122, 122+116, s)-Nets in Base 3
(122, 122+116, 78)-Net over F3 — Constructive and digital
Digital (122, 238, 78)-net over F3, using
- t-expansion [i] based on digital (121, 238, 78)-net over F3, using
- net from sequence [i] based on digital (121, 77)-sequence over F3, using
- base reduction for sequences [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
- base reduction for sequences [i] based on digital (22, 77)-sequence over F9, using
- net from sequence [i] based on digital (121, 77)-sequence over F3, using
(122, 122+116, 125)-Net over F3 — Digital
Digital (122, 238, 125)-net over F3, using
(122, 122+116, 962)-Net in Base 3 — Upper bound on s
There is no (122, 238, 963)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 369254 030282 263565 900035 695483 015292 951129 276624 658881 991750 348865 263440 506152 528954 094964 576278 275856 950017 647349 > 3238 [i]