Best Known (246−90, 246, s)-Nets in Base 4
(246−90, 246, 160)-Net over F4 — Constructive and digital
Digital (156, 246, 160)-net over F4, using
- 10 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
(246−90, 246, 196)-Net in Base 4 — Constructive
(156, 246, 196)-net in base 4, using
- 2 times m-reduction [i] based on (156, 248, 196)-net in base 4, using
- trace code for nets [i] based on (32, 124, 98)-net in base 16, using
- 1 times m-reduction [i] based on (32, 125, 98)-net in base 16, using
- base change [i] based on digital (7, 100, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- base change [i] based on digital (7, 100, 98)-net over F32, using
- 1 times m-reduction [i] based on (32, 125, 98)-net in base 16, using
- trace code for nets [i] based on (32, 124, 98)-net in base 16, using
(246−90, 246, 475)-Net over F4 — Digital
Digital (156, 246, 475)-net over F4, using
(246−90, 246, 11452)-Net in Base 4 — Upper bound on s
There is no (156, 246, 11453)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 12792 882425 425586 140549 654106 611201 911211 113550 354589 425931 071571 641160 537515 052131 685713 293572 272384 303913 479123 361614 409554 573924 694144 323242 600388 > 4246 [i]