Best Known (106−59, 106, s)-Nets in Base 9
(106−59, 106, 96)-Net over F9 — Constructive and digital
Digital (47, 106, 96)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 34, 32)-net over F9, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 5 and N(F) ≥ 32, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- digital (13, 72, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- digital (5, 34, 32)-net over F9, using
(106−59, 106, 162)-Net over F9 — Digital
Digital (47, 106, 162)-net over F9, using
- t-expansion [i] based on digital (46, 106, 162)-net over F9, using
- net from sequence [i] based on digital (46, 161)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 46 and N(F) ≥ 162, using
- net from sequence [i] based on digital (46, 161)-sequence over F9, using
(106−59, 106, 4141)-Net in Base 9 — Upper bound on s
There is no (47, 106, 4142)-net in base 9, because
- 1 times m-reduction [i] would yield (47, 105, 4142)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 15688 271280 317467 904121 119341 572236 518958 357673 316619 011959 928909 631026 466759 562994 425439 429638 079281 > 9105 [i]