Best Known (154, 154+87, s)-Nets in Base 4
(154, 154+87, 160)-Net over F4 — Constructive and digital
Digital (154, 241, 160)-net over F4, using
- 9 times m-reduction [i] based on digital (154, 250, 160)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (33, 81, 56)-net over F4, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- F5 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) = 33 and N(F) ≥ 56, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- digital (73, 169, 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 (33, 81, 56)-net over F4, using
- (u, u+v)-construction [i] based on
(154, 154+87, 208)-Net in Base 4 — Constructive
(154, 241, 208)-net in base 4, using
- 41 times duplication [i] based on (153, 240, 208)-net in base 4, using
- trace code for nets [i] based on (33, 120, 104)-net in base 16, using
- base change [i] based on digital (9, 96, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- base change [i] based on digital (9, 96, 104)-net over F32, using
- trace code for nets [i] based on (33, 120, 104)-net in base 16, using
(154, 154+87, 489)-Net over F4 — Digital
Digital (154, 241, 489)-net over F4, using
(154, 154+87, 12867)-Net in Base 4 — Upper bound on s
There is no (154, 241, 12868)-net in base 4, because
- 1 times m-reduction [i] would yield (154, 240, 12868)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 3 127491 396607 128975 666365 186455 951612 269875 905655 708655 497748 842750 228321 445654 777239 849974 100746 083588 011648 347991 005961 824122 390130 712648 884120 > 4240 [i]