Best Known (177−61, 177, s)-Nets in Base 4
(177−61, 177, 160)-Net over F4 — Constructive and digital
Digital (116, 177, 160)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (13, 43, 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 (73, 134, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 67, 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, 67, 65)-net over F16, using
- digital (13, 43, 30)-net over F4, using
(177−61, 177, 208)-Net in Base 4 — Constructive
(116, 177, 208)-net in base 4, using
- 1 times m-reduction [i] based on (116, 178, 208)-net in base 4, using
- trace code for nets [i] based on (27, 89, 104)-net in base 16, using
- 1 times m-reduction [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
- 1 times m-reduction [i] based on (27, 90, 104)-net in base 16, using
- trace code for nets [i] based on (27, 89, 104)-net in base 16, using
(177−61, 177, 438)-Net over F4 — Digital
Digital (116, 177, 438)-net over F4, using
(177−61, 177, 13645)-Net in Base 4 — Upper bound on s
There is no (116, 177, 13646)-net in base 4, because
- 1 times m-reduction [i] would yield (116, 176, 13646)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 9193 766482 638817 592697 258120 739343 343798 269206 779283 469484 487300 095447 735520 493778 349872 888089 150881 030144 > 4176 [i]