Best Known (133, 228, s)-Nets in Base 4
(133, 228, 134)-Net over F4 — Constructive and digital
Digital (133, 228, 134)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (13, 60, 30)-net over F4, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 30, using
- F4 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) = 13 and N(F) ≥ 30, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- digital (73, 168, 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 (13, 60, 30)-net over F4, using
(133, 228, 288)-Net over F4 — Digital
Digital (133, 228, 288)-net over F4, using
(133, 228, 4913)-Net in Base 4 — Upper bound on s
There is no (133, 228, 4914)-net in base 4, because
- 1 times m-reduction [i] would yield (133, 227, 4914)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 46665 369857 511537 861735 379471 461823 264965 770359 956233 237402 395273 435909 094680 281019 025633 583868 842522 725487 876757 423998 113323 141965 039400 > 4227 [i]