Best Known (18, 18+44, s)-Nets in Base 8
(18, 18+44, 65)-Net over F8 — Constructive and digital
Digital (18, 62, 65)-net over F8, using
- t-expansion [i] based on digital (14, 62, 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
(18, 18+44, 440)-Net in Base 8 — Upper bound on s
There is no (18, 62, 441)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 101 740969 736812 036129 413531 101678 628990 037805 988206 727292 > 862 [i]