Best Known (102−55, 102, s)-Nets in Base 9
(102−55, 102, 102)-Net over F9 — Constructive and digital
Digital (47, 102, 102)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 30, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-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 (3, 30, 28)-net over F9, using
(102−55, 102, 162)-Net over F9 — Digital
Digital (47, 102, 162)-net over F9, using
- t-expansion [i] based on digital (46, 102, 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
(102−55, 102, 5052)-Net in Base 9 — Upper bound on s
There is no (47, 102, 5053)-net in base 9, because
- 1 times m-reduction [i] would yield (47, 101, 5053)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 2 399826 513070 572455 249469 872484 888128 889705 238996 719368 238609 097875 920171 007517 659100 037917 240505 > 9101 [i]