Best Known (108, 157, s)-Nets in Base 3
(108, 157, 156)-Net over F3 — Constructive and digital
Digital (108, 157, 156)-net over F3, using
- 15 times m-reduction [i] based on digital (108, 172, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 86, 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
- trace code for nets [i] based on digital (22, 86, 78)-net over F9, using
(108, 157, 318)-Net over F3 — Digital
Digital (108, 157, 318)-net over F3, using
(108, 157, 6165)-Net in Base 3 — Upper bound on s
There is no (108, 157, 6166)-net in base 3, because
- 1 times m-reduction [i] would yield (108, 156, 6166)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 270 199869 769738 624160 270707 174586 658230 522708 880276 239986 092409 218850 558833 > 3156 [i]