Best Known (236−84, 236, s)-Nets in Base 4
(236−84, 236, 160)-Net over F4 — Constructive and digital
Digital (152, 236, 160)-net over F4, using
- 8 times m-reduction [i] based on digital (152, 244, 160)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (33, 79, 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, 165, 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, 79, 56)-net over F4, using
- (u, u+v)-construction [i] based on
(236−84, 236, 208)-Net in Base 4 — Constructive
(152, 236, 208)-net in base 4, using
- 2 times m-reduction [i] based on (152, 238, 208)-net in base 4, using
- trace code for nets [i] based on (33, 119, 104)-net in base 16, using
- 1 times m-reduction [i] based on (33, 120, 104)-net in base 16, using
- base change [i] based on digital (9, 96, 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, 96, 104)-net over F32, using
- 1 times m-reduction [i] based on (33, 120, 104)-net in base 16, using
- trace code for nets [i] based on (33, 119, 104)-net in base 16, using
(236−84, 236, 505)-Net over F4 — Digital
Digital (152, 236, 505)-net over F4, using
(236−84, 236, 13260)-Net in Base 4 — Upper bound on s
There is no (152, 236, 13261)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 12216 978389 905679 890580 400843 655659 332169 269792 691952 705657 379665 309680 256238 309929 498201 303301 458461 793395 289207 698761 827670 419445 112349 185220 > 4236 [i]