Best Known (236−96, 236, s)-Nets in Base 3
(236−96, 236, 156)-Net over F3 — Constructive and digital
Digital (140, 236, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 118, 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
(236−96, 236, 206)-Net over F3 — Digital
Digital (140, 236, 206)-net over F3, using
(236−96, 236, 2030)-Net in Base 3 — Upper bound on s
There is no (140, 236, 2031)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 40090 789230 367925 303316 444546 869979 265555 639346 341324 311021 990102 329189 217416 634924 831998 744727 991744 616190 440865 > 3236 [i]