Best Known (128−42, 128, s)-Nets in Base 3
(128−42, 128, 156)-Net over F3 — Constructive and digital
Digital (86, 128, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 64, 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
(128−42, 128, 230)-Net over F3 — Digital
Digital (86, 128, 230)-net over F3, using
(128−42, 128, 3492)-Net in Base 3 — Upper bound on s
There is no (86, 128, 3493)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 11 849379 870111 435233 328437 790588 639037 454097 144230 928940 909851 > 3128 [i]