Best Known (210−125, 210, s)-Nets in Base 4
(210−125, 210, 104)-Net over F4 — Constructive and digital
Digital (85, 210, 104)-net over F4, using
- t-expansion [i] based on digital (73, 210, 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
(210−125, 210, 129)-Net over F4 — Digital
Digital (85, 210, 129)-net over F4, using
- t-expansion [i] based on digital (81, 210, 129)-net over F4, using
- net from sequence [i] based on digital (81, 128)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 81 and N(F) ≥ 129, using
- net from sequence [i] based on digital (81, 128)-sequence over F4, using
(210−125, 210, 803)-Net in Base 4 — Upper bound on s
There is no (85, 210, 804)-net in base 4, because
- 1 times m-reduction [i] would yield (85, 209, 804)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 683911 159821 516055 614266 339094 011959 874712 502165 262937 179004 092861 967682 163874 063726 561823 423273 810266 991755 855437 318489 024320 > 4209 [i]