Best Known (73, 73+71, s)-Nets in Base 8
(73, 73+71, 160)-Net over F8 — Constructive and digital
Digital (73, 144, 160)-net over F8, using
- trace code for nets [i] based on digital (1, 72, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
(73, 73+71, 249)-Net over F8 — Digital
Digital (73, 144, 249)-net over F8, using
(73, 73+71, 9703)-Net in Base 8 — Upper bound on s
There is no (73, 144, 9704)-net in base 8, because
- 1 times m-reduction [i] would yield (73, 143, 9704)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 1386 354361 547856 916259 193945 361990 037265 421670 952623 912115 462705 082361 144963 877008 832347 668705 579888 133706 372114 978511 325454 278831 > 8143 [i]