Best Known (72, 161, s)-Nets in Base 8
(72, 161, 130)-Net over F8 — Constructive and digital
Digital (72, 161, 130)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (14, 58, 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 (14, 103, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8 (see above)
- digital (14, 58, 65)-net over F8, using
(72, 161, 173)-Net over F8 — Digital
Digital (72, 161, 173)-net over F8, using
(72, 161, 4712)-Net in Base 8 — Upper bound on s
There is no (72, 161, 4713)-net in base 8, because
- 1 times m-reduction [i] would yield (72, 160, 4713)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 3 139997 910523 341567 425102 394334 639202 044668 636659 142710 206508 079739 029317 867567 845599 577263 420022 958071 604688 872529 690705 475827 984188 720965 240176 > 8160 [i]