Best Known (18, 18+33, s)-Nets in Base 8
(18, 18+33, 65)-Net over F8 — Constructive and digital
Digital (18, 51, 65)-net over F8, using
- t-expansion [i] based on digital (14, 51, 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+33, 635)-Net in Base 8 — Upper bound on s
There is no (18, 51, 636)-net in base 8, because
- 1 times m-reduction [i] would yield (18, 50, 636)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 1451 655123 162099 688850 524361 396399 265433 413333 > 850 [i]