Best Known (136−77, 136, s)-Nets in Base 8
(136−77, 136, 99)-Net over F8 — Constructive and digital
Digital (59, 136, 99)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 45, 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, 91, 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, 45, 34)-net over F8, using
(136−77, 136, 144)-Net over F8 — Digital
Digital (59, 136, 144)-net over F8, using
- t-expansion [i] based on digital (45, 136, 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
(136−77, 136, 3443)-Net in Base 8 — Upper bound on s
There is no (59, 136, 3444)-net in base 8, because
- 1 times m-reduction [i] would yield (59, 135, 3444)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 82 723938 178322 532557 873714 316919 922800 225910 111588 312083 535783 816475 680033 574923 629655 957081 107319 020114 106055 178195 952460 > 8135 [i]