Best Known (134, 217, s)-Nets in Base 4
(134, 217, 137)-Net over F4 — Constructive and digital
Digital (134, 217, 137)-net over F4, using
- 9 times m-reduction [i] based on digital (134, 226, 137)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (15, 61, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- digital (73, 165, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- digital (15, 61, 33)-net over F4, using
- (u, u+v)-construction [i] based on
(134, 217, 365)-Net over F4 — Digital
Digital (134, 217, 365)-net over F4, using
(134, 217, 7957)-Net in Base 4 — Upper bound on s
There is no (134, 217, 7958)-net in base 4, because
- 1 times m-reduction [i] would yield (134, 216, 7958)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 11105 892733 582657 914063 298245 762492 607724 518067 073625 546478 587646 174766 383472 479854 219911 117560 048875 364456 255852 377729 490652 967600 > 4216 [i]