Best Known (72−36, 72, s)-Nets in Base 9
(72−36, 72, 164)-Net over F9 — Constructive and digital
Digital (36, 72, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 36, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
(72−36, 72, 6183)-Net in Base 9 — Upper bound on s
There is no (36, 72, 6184)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 507 808240 454412 916484 027050 104637 700501 391280 822471 087864 256493 165441 > 972 [i]