Best Known (61, 122, s)-Nets in Base 9
(61, 122, 164)-Net over F9 — Constructive and digital
Digital (61, 122, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 61, 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
(61, 122, 233)-Net over F9 — Digital
Digital (61, 122, 233)-net over F9, using
(61, 122, 10610)-Net in Base 9 — Upper bound on s
There is no (61, 122, 10611)-net in base 9, because
- 1 times m-reduction [i] would yield (61, 121, 10611)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 29 114331 460761 565825 525422 255580 711280 255199 468536 757360 533586 760369 231803 278001 038678 319047 813474 623288 665028 447825 > 9121 [i]