Best Known (159−74, 159, s)-Nets in Base 4
(159−74, 159, 104)-Net over F4 — Constructive and digital
Digital (85, 159, 104)-net over F4, using
- t-expansion [i] based on digital (73, 159, 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
(159−74, 159, 148)-Net over F4 — Digital
Digital (85, 159, 148)-net over F4, using
(159−74, 159, 1857)-Net in Base 4 — Upper bound on s
There is no (85, 159, 1858)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 534665 910682 571605 950116 957463 899398 866445 918382 721531 408969 466762 843989 866402 530045 020103 697200 > 4159 [i]