Best Known (97, 97+48, s)-Nets in Base 3
(97, 97+48, 156)-Net over F3 — Constructive and digital
Digital (97, 145, 156)-net over F3, using
- 5 times m-reduction [i] based on digital (97, 150, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 75, 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, 75, 78)-net over F9, using
(97, 97+48, 249)-Net over F3 — Digital
Digital (97, 145, 249)-net over F3, using
(97, 97+48, 3717)-Net in Base 3 — Upper bound on s
There is no (97, 145, 3718)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1530 878936 121134 122352 147079 674644 049039 025161 621012 763901 480485 796977 > 3145 [i]