Best Known (73, 73+69, s)-Nets in Base 4
(73, 73+69, 104)-Net over F4 — Constructive and digital
Digital (73, 142, 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
(73, 73+69, 117)-Net over F4 — Digital
Digital (73, 142, 117)-net over F4, using
(73, 73+69, 1388)-Net in Base 4 — Upper bound on s
There is no (73, 142, 1389)-net in base 4, because
- 1 times m-reduction [i] would yield (73, 141, 1389)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 7 845672 790115 119655 415917 632641 104868 354964 674186 129814 710352 122503 679491 258889 173350 > 4141 [i]