Best Known (18, 18+35, s)-Nets in Base 8
(18, 18+35, 65)-Net over F8 — Constructive and digital
Digital (18, 53, 65)-net over F8, using
- t-expansion [i] based on digital (14, 53, 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+35, 582)-Net in Base 8 — Upper bound on s
There is no (18, 53, 583)-net in base 8, because
- 1 times m-reduction [i] would yield (18, 52, 583)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 91653 621030 801111 799412 027861 063848 172411 815512 > 852 [i]