Best Known (72−53, 72, s)-Nets in Base 8
(72−53, 72, 65)-Net over F8 — Constructive and digital
Digital (19, 72, 65)-net over F8, using
- t-expansion [i] based on digital (14, 72, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
(72−53, 72, 424)-Net in Base 8 — Upper bound on s
There is no (19, 72, 425)-net in base 8, because
- 1 times m-reduction [i] would yield (19, 71, 425)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 13279 333455 396290 911440 234184 484843 396683 281491 318771 294865 563120 > 871 [i]