Best Known (104−57, 104, s)-Nets in Base 9
(104−57, 104, 98)-Net over F9 — Constructive and digital
Digital (47, 104, 98)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 34, 34)-net over F9, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 6 and N(F) ≥ 34, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- digital (13, 70, 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 (6, 34, 34)-net over F9, using
(104−57, 104, 162)-Net over F9 — Digital
Digital (47, 104, 162)-net over F9, using
- t-expansion [i] based on digital (46, 104, 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
(104−57, 104, 4555)-Net in Base 9 — Upper bound on s
There is no (47, 104, 4556)-net in base 9, because
- 1 times m-reduction [i] would yield (47, 103, 4556)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 194 071893 936000 420909 391341 882584 089108 511120 926326 644392 891662 295094 819965 199336 644897 000130 616705 > 9103 [i]