Best Known (181−62, 181, s)-Nets in Base 4
(181−62, 181, 160)-Net over F4 — Constructive and digital
Digital (119, 181, 160)-net over F4, using
- 1 times m-reduction [i] based on digital (119, 182, 160)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (13, 44, 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 (75, 138, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 69, 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, 69, 65)-net over F16, using
- digital (13, 44, 30)-net over F4, using
- (u, u+v)-construction [i] based on
(181−62, 181, 208)-Net in Base 4 — Constructive
(119, 181, 208)-net in base 4, using
- 41 times duplication [i] based on (118, 180, 208)-net in base 4, using
- t-expansion [i] based on (117, 180, 208)-net in base 4, using
- trace code for nets [i] based on (27, 90, 104)-net in base 16, using
- base change [i] based on digital (9, 72, 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, 72, 104)-net over F32, using
- trace code for nets [i] based on (27, 90, 104)-net in base 16, using
- t-expansion [i] based on (117, 180, 208)-net in base 4, using
(181−62, 181, 457)-Net over F4 — Digital
Digital (119, 181, 457)-net over F4, using
(181−62, 181, 13531)-Net in Base 4 — Upper bound on s
There is no (119, 181, 13532)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 9 399864 134152 514893 663202 608480 418846 537189 653826 697952 833950 881299 197449 608618 716214 853914 267447 874865 218288 > 4181 [i]