Best Known (78, 78+34, s)-Nets in Base 3
(78, 78+34, 156)-Net over F3 — Constructive and digital
Digital (78, 112, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 56, 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
(78, 78+34, 265)-Net over F3 — Digital
Digital (78, 112, 265)-net over F3, using
(78, 78+34, 4975)-Net in Base 3 — Upper bound on s
There is no (78, 112, 4976)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 274040 627768 657972 959044 170285 965293 714565 777150 875873 > 3112 [i]