Best Known (17, 17+29, s)-Nets in Base 8
(17, 17+29, 65)-Net over F8 — Constructive and digital
Digital (17, 46, 65)-net over F8, using
- t-expansion [i] based on digital (14, 46, 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
(17, 17+29, 682)-Net in Base 8 — Upper bound on s
There is no (17, 46, 683)-net in base 8, because
- 1 times m-reduction [i] would yield (17, 45, 683)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 44438 964911 475291 523137 055775 149746 843064 > 845 [i]