Best Known (55, 110, s)-Nets in Base 9
(55, 110, 164)-Net over F9 — Constructive and digital
Digital (55, 110, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 55, 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
(55, 110, 214)-Net over F9 — Digital
Digital (55, 110, 214)-net over F9, using
(55, 110, 9702)-Net in Base 9 — Upper bound on s
There is no (55, 110, 9703)-net in base 9, because
- 1 times m-reduction [i] would yield (55, 109, 9703)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 102 960849 588130 964524 127057 166319 037918 155097 382994 487662 126843 486793 010786 206113 961115 679636 846552 922089 > 9109 [i]