Best Known (18, 18+29, s)-Nets in Base 8
(18, 18+29, 65)-Net over F8 — Constructive and digital
Digital (18, 47, 65)-net over F8, using
- t-expansion [i] based on digital (14, 47, 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+29, 792)-Net in Base 8 — Upper bound on s
There is no (18, 47, 793)-net in base 8, because
- 1 times m-reduction [i] would yield (18, 46, 793)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 351072 608696 469863 939404 502613 814594 285608 > 846 [i]