Best Known (134, 134+73, s)-Nets in Base 4
(134, 134+73, 160)-Net over F4 — Constructive and digital
Digital (134, 207, 160)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (13, 49, 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 (85, 158, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 79, 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, 79, 65)-net over F16, using
- digital (13, 49, 30)-net over F4, using
(134, 134+73, 208)-Net in Base 4 — Constructive
(134, 207, 208)-net in base 4, using
- 1 times m-reduction [i] based on (134, 208, 208)-net in base 4, using
- trace code for nets [i] based on (30, 104, 104)-net in base 16, using
- 1 times m-reduction [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
- 1 times m-reduction [i] based on (30, 105, 104)-net in base 16, using
- trace code for nets [i] based on (30, 104, 104)-net in base 16, using
(134, 134+73, 464)-Net over F4 — Digital
Digital (134, 207, 464)-net over F4, using
(134, 134+73, 13236)-Net in Base 4 — Upper bound on s
There is no (134, 207, 13237)-net in base 4, because
- 1 times m-reduction [i] would yield (134, 206, 13237)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 10593 254310 979665 935648 042772 947146 602178 923691 081507 911865 994870 799321 744889 737813 664456 464772 166309 772375 652159 891322 603551 > 4206 [i]