Best Known (74, 74+65, s)-Nets in Base 4
(74, 74+65, 104)-Net over F4 — Constructive and digital
Digital (74, 139, 104)-net over F4, using
- t-expansion [i] based on digital (73, 139, 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
(74, 74+65, 130)-Net over F4 — Digital
Digital (74, 139, 130)-net over F4, using
(74, 74+65, 1657)-Net in Base 4 — Upper bound on s
There is no (74, 139, 1658)-net in base 4, because
- 1 times m-reduction [i] would yield (74, 138, 1658)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 123240 081474 300045 144010 342633 252960 477482 096134 364052 463049 849630 758214 270119 392717 > 4138 [i]