Best Known (80−40, 80, s)-Nets in Base 9
(80−40, 80, 164)-Net over F9 — Constructive and digital
Digital (40, 80, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 40, 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
(80−40, 80, 166)-Net over F9 — Digital
Digital (40, 80, 166)-net over F9, using
(80−40, 80, 6798)-Net in Base 9 — Upper bound on s
There is no (40, 80, 6799)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 21871 804661 676501 493315 938934 168309 882939 431223 526488 730470 177509 239883 824481 > 980 [i]