Best Known (107−55, 107, s)-Nets in Base 9
(107−55, 107, 114)-Net over F9 — Constructive and digital
Digital (52, 107, 114)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (8, 35, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- digital (17, 72, 74)-net over F9, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- digital (8, 35, 40)-net over F9, using
(107−55, 107, 186)-Net over F9 — Digital
Digital (52, 107, 186)-net over F9, using
(107−55, 107, 7597)-Net in Base 9 — Upper bound on s
There is no (52, 107, 7598)-net in base 9, because
- 1 times m-reduction [i] would yield (52, 106, 7598)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 141434 648625 408899 329885 148893 759683 563751 785201 033393 278058 309490 479502 327975 191665 062970 730019 800209 > 9106 [i]