Best Known (157, 157+88, s)-Nets in Base 4
(157, 157+88, 160)-Net over F4 — Constructive and digital
Digital (157, 245, 160)-net over F4, using
- 14 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
(157, 157+88, 208)-Net in Base 4 — Constructive
(157, 245, 208)-net in base 4, using
- 1 times m-reduction [i] based on (157, 246, 208)-net in base 4, using
- trace code for nets [i] based on (34, 123, 104)-net in base 16, using
- 2 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
- 2 times m-reduction [i] based on (34, 125, 104)-net in base 16, using
- trace code for nets [i] based on (34, 123, 104)-net in base 16, using
(157, 157+88, 505)-Net over F4 — Digital
Digital (157, 245, 505)-net over F4, using
(157, 157+88, 12911)-Net in Base 4 — Upper bound on s
There is no (157, 245, 12912)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3205 111898 704953 364906 846134 940336 372554 074216 357920 737750 404145 914336 551531 934043 606098 134002 285343 486320 066447 129966 619140 303697 916795 292122 274385 > 4245 [i]