Best Known (115, 115+68, s)-Nets in Base 3
(115, 115+68, 156)-Net over F3 — Constructive and digital
Digital (115, 183, 156)-net over F3, using
- 3 times m-reduction [i] based on digital (115, 186, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 93, 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, 93, 78)-net over F9, using
(115, 115+68, 214)-Net over F3 — Digital
Digital (115, 183, 214)-net over F3, using
(115, 115+68, 2469)-Net in Base 3 — Upper bound on s
There is no (115, 183, 2470)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2062 419798 874613 085784 006821 403643 417792 463683 821057 629414 304574 449324 174547 055753 604461 > 3183 [i]