Best Known (55, 55+69, s)-Nets in Base 8
(55, 55+69, 99)-Net over F8 — Constructive and digital
Digital (55, 124, 99)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 41, 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, 83, 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, 41, 34)-net over F8, using
(55, 55+69, 144)-Net over F8 — Digital
Digital (55, 124, 144)-net over F8, using
- t-expansion [i] based on digital (45, 124, 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
(55, 55+69, 3555)-Net in Base 8 — Upper bound on s
There is no (55, 124, 3556)-net in base 8, because
- 1 times m-reduction [i] would yield (55, 123, 3556)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 1213 741331 975790 232567 873793 896078 188201 353202 709586 914757 653512 706682 304730 119991 372197 915596 642348 827395 141305 > 8123 [i]