Best Known (151, 240, s)-Nets in Base 4
(151, 240, 160)-Net over F4 — Constructive and digital
Digital (151, 240, 160)-net over F4, using
- 1 times m-reduction [i] based on digital (151, 241, 160)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (33, 78, 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, 163, 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, 78, 56)-net over F4, using
- (u, u+v)-construction [i] based on
(151, 240, 196)-Net in Base 4 — Constructive
(151, 240, 196)-net in base 4, using
- trace code for nets [i] based on (31, 120, 98)-net in base 16, using
- base change [i] based on digital (7, 96, 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, 96, 98)-net over F32, using
(151, 240, 443)-Net over F4 — Digital
Digital (151, 240, 443)-net over F4, using
(151, 240, 10681)-Net in Base 4 — Upper bound on s
There is no (151, 240, 10682)-net in base 4, because
- 1 times m-reduction [i] would yield (151, 239, 10682)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 783348 341088 894848 613296 032724 148245 339645 544645 809009 352857 369031 032239 814085 436919 750897 364076 292761 247487 273238 886821 485293 990571 145011 021700 > 4239 [i]