Best Known (121, 121+62, s)-Nets in Base 3
(121, 121+62, 156)-Net over F3 — Constructive and digital
Digital (121, 183, 156)-net over F3, using
- 15 times m-reduction [i] based on digital (121, 198, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 99, 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, 99, 78)-net over F9, using
(121, 121+62, 281)-Net over F3 — Digital
Digital (121, 183, 281)-net over F3, using
(121, 121+62, 4039)-Net in Base 3 — Upper bound on s
There is no (121, 183, 4040)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2068 588349 590764 233472 802819 707605 400734 121156 942391 918435 304590 167305 634852 697675 372385 > 3183 [i]