Best Known (156−56, 156, s)-Nets in Base 3
(156−56, 156, 156)-Net over F3 — Constructive and digital
Digital (100, 156, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 78, 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
(156−56, 156, 206)-Net over F3 — Digital
Digital (100, 156, 206)-net over F3, using
(156−56, 156, 2544)-Net in Base 3 — Upper bound on s
There is no (100, 156, 2545)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 271 689178 346406 712572 333389 372511 843294 389926 456374 370950 309172 197950 197425 > 3156 [i]