Best Known (242−87, 242, s)-Nets in Base 4
(242−87, 242, 160)-Net over F4 — Constructive and digital
Digital (155, 242, 160)-net over F4, using
- 11 times m-reduction [i] based on digital (155, 253, 160)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (33, 82, 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, 171, 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, 82, 56)-net over F4, using
- (u, u+v)-construction [i] based on
(242−87, 242, 208)-Net in Base 4 — Constructive
(155, 242, 208)-net in base 4, using
- 42 times duplication [i] based on (153, 240, 208)-net in base 4, using
- trace code for nets [i] based on (33, 120, 104)-net in base 16, using
- base change [i] based on digital (9, 96, 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, 96, 104)-net over F32, using
- trace code for nets [i] based on (33, 120, 104)-net in base 16, using
(242−87, 242, 498)-Net over F4 — Digital
Digital (155, 242, 498)-net over F4, using
(242−87, 242, 13290)-Net in Base 4 — Upper bound on s
There is no (155, 242, 13291)-net in base 4, because
- 1 times m-reduction [i] would yield (155, 241, 13291)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 12 519182 090367 598199 247098 350759 764222 986619 005415 145856 822413 102466 180403 341332 613030 809038 557190 428935 674278 633381 835259 376808 337215 304107 971236 > 4241 [i]