Best Known (50, 109, s)-Nets in Base 8
(50, 109, 99)-Net over F8 — Constructive and digital
Digital (50, 109, 99)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 36, 34)-net over F8, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- digital (14, 73, 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
- digital (7, 36, 34)-net over F8, using
(50, 109, 144)-Net over F8 — Digital
Digital (50, 109, 144)-net over F8, using
- t-expansion [i] based on digital (45, 109, 144)-net over F8, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 45 and N(F) ≥ 144, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
(50, 109, 3830)-Net in Base 8 — Upper bound on s
There is no (50, 109, 3831)-net in base 8, because
- 1 times m-reduction [i] would yield (50, 108, 3831)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 34 417179 155575 902985 946580 078730 728215 232480 746692 694514 296441 850913 465493 554425 161833 557136 066904 > 8108 [i]