Best Known (254−94, 254, s)-Nets in Base 4
(254−94, 254, 160)-Net over F4 — Constructive and digital
Digital (160, 254, 160)-net over F4, using
- t-expansion [i] based on digital (157, 254, 160)-net over F4, using
- 5 times m-reduction [i] based on digital (157, 259, 160)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (33, 84, 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, 175, 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, 84, 56)-net over F4, using
- (u, u+v)-construction [i] based on
- 5 times m-reduction [i] based on digital (157, 259, 160)-net over F4, using
(254−94, 254, 196)-Net in Base 4 — Constructive
(160, 254, 196)-net in base 4, using
- trace code for nets [i] based on (33, 127, 98)-net in base 16, using
- 3 times m-reduction [i] based on (33, 130, 98)-net in base 16, using
- base change [i] based on digital (7, 104, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- base change [i] based on digital (7, 104, 98)-net over F32, using
- 3 times m-reduction [i] based on (33, 130, 98)-net in base 16, using
(254−94, 254, 469)-Net over F4 — Digital
Digital (160, 254, 469)-net over F4, using
(254−94, 254, 10942)-Net in Base 4 — Upper bound on s
There is no (160, 254, 10943)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 838 190629 967137 045534 601884 144567 340466 750229 298700 165178 379737 792191 997808 375656 585541 220676 886714 734232 202813 039456 065070 718849 371491 726429 030180 521420 > 4254 [i]