Best Known (211−74, 211, s)-Nets in Base 4
(211−74, 211, 160)-Net over F4 — Constructive and digital
Digital (137, 211, 160)-net over F4, using
- 1 times m-reduction [i] based on digital (137, 212, 160)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (13, 50, 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 (87, 162, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 81, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 81, 65)-net over F16, using
- digital (13, 50, 30)-net over F4, using
- (u, u+v)-construction [i] based on
(211−74, 211, 208)-Net in Base 4 — Constructive
(137, 211, 208)-net in base 4, using
- 41 times duplication [i] based on (136, 210, 208)-net in base 4, using
- t-expansion [i] based on (135, 210, 208)-net in base 4, using
- trace code for nets [i] based on (30, 105, 104)-net in base 16, using
- base change [i] based on digital (9, 84, 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, 84, 104)-net over F32, using
- trace code for nets [i] based on (30, 105, 104)-net in base 16, using
- t-expansion [i] based on (135, 210, 208)-net in base 4, using
(211−74, 211, 481)-Net over F4 — Digital
Digital (137, 211, 481)-net over F4, using
(211−74, 211, 13217)-Net in Base 4 — Upper bound on s
There is no (137, 211, 13218)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 10 831370 152033 292864 736832 601974 409255 069933 384286 454859 192016 338696 605728 105077 087274 019577 188175 011592 777330 899574 154929 260000 > 4211 [i]