Best Known (156, 156+88, s)-Nets in Base 4
(156, 156+88, 160)-Net over F4 — Constructive and digital
Digital (156, 244, 160)-net over F4, using
- 12 times m-reduction [i] based on digital (156, 256, 160)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (33, 83, 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, 173, 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, 83, 56)-net over F4, using
- (u, u+v)-construction [i] based on
(156, 156+88, 208)-Net in Base 4 — Constructive
(156, 244, 208)-net in base 4, using
- trace code for nets [i] based on (34, 122, 104)-net in base 16, using
- 3 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
- 3 times m-reduction [i] based on (34, 125, 104)-net in base 16, using
(156, 156+88, 496)-Net over F4 — Digital
Digital (156, 244, 496)-net over F4, using
(156, 156+88, 12509)-Net in Base 4 — Upper bound on s
There is no (156, 244, 12510)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 800 131625 679919 591948 162146 862913 029055 867189 380104 007162 193419 179027 730344 974997 438842 795915 699571 114484 655520 040199 920659 935221 746151 270792 621282 > 4244 [i]