Best Known (59, 118, s)-Nets in Base 9
(59, 118, 164)-Net over F9 — Constructive and digital
Digital (59, 118, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 59, 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
(59, 118, 226)-Net over F9 — Digital
Digital (59, 118, 226)-net over F9, using
(59, 118, 10307)-Net in Base 9 — Upper bound on s
There is no (59, 118, 10308)-net in base 9, because
- 1 times m-reduction [i] would yield (59, 117, 10308)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 4432 349916 639684 094722 155068 946971 676116 161926 176188 568109 871220 154210 328785 332566 168466 378332 284722 070660 506785 > 9117 [i]