Best Known (246−88, 246, s)-Nets in Base 4
(246−88, 246, 160)-Net over F4 — Constructive and digital
Digital (158, 246, 160)-net over F4, using
- t-expansion [i] based on digital (157, 246, 160)-net over F4, using
- 13 times m-reduction [i] based on digital (157, 259, 160)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (33, 84, 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, 175, 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, 84, 56)-net over F4, using
- (u, u+v)-construction [i] based on
- 13 times m-reduction [i] based on digital (157, 259, 160)-net over F4, using
(246−88, 246, 208)-Net in Base 4 — Constructive
(158, 246, 208)-net in base 4, using
- 2 times m-reduction [i] based on (158, 248, 208)-net in base 4, using
- trace code for nets [i] based on (34, 124, 104)-net in base 16, using
- 1 times m-reduction [i] based on (34, 125, 104)-net in base 16, using
- base change [i] based on digital (9, 100, 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, 100, 104)-net over F32, using
- 1 times m-reduction [i] based on (34, 125, 104)-net in base 16, using
- trace code for nets [i] based on (34, 124, 104)-net in base 16, using
(246−88, 246, 514)-Net over F4 — Digital
Digital (158, 246, 514)-net over F4, using
(246−88, 246, 13325)-Net in Base 4 — Upper bound on s
There is no (158, 246, 13326)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 12801 628684 051097 306102 119161 333858 092906 388533 573383 555844 167314 876615 169289 610554 978719 195206 602732 599128 714624 017449 528746 400436 711366 777968 696672 > 4246 [i]