Best Known (159, 159+91, s)-Nets in Base 4
(159, 159+91, 160)-Net over F4 — Constructive and digital
Digital (159, 250, 160)-net over F4, using
- t-expansion [i] based on digital (157, 250, 160)-net over F4, using
- 9 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
- 9 times m-reduction [i] based on digital (157, 259, 160)-net over F4, using
(159, 159+91, 208)-Net in Base 4 — Constructive
(159, 250, 208)-net in base 4, using
- trace code for nets [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
(159, 159+91, 490)-Net over F4 — Digital
Digital (159, 250, 490)-net over F4, using
(159, 159+91, 12565)-Net in Base 4 — Upper bound on s
There is no (159, 250, 12566)-net in base 4, because
- 1 times m-reduction [i] would yield (159, 249, 12566)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 820176 498014 994944 502036 762987 733679 338574 829930 474365 233264 799100 735505 806740 871429 374780 930110 511176 007559 226779 423796 003664 660703 918684 687598 312720 > 4249 [i]