Best Known (57−42, 57, s)-Nets in Base 8
(57−42, 57, 65)-Net over F8 — Constructive and digital
Digital (15, 57, 65)-net over F8, using
- t-expansion [i] based on digital (14, 57, 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
(57−42, 57, 337)-Net in Base 8 — Upper bound on s
There is no (15, 57, 338)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 3064 247301 760309 064250 017531 516510 749784 149755 733008 > 857 [i]