Best Known (125−67, 125, s)-Nets in Base 9
(125−67, 125, 114)-Net over F9 — Constructive and digital
Digital (58, 125, 114)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (8, 41, 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, 84, 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, 41, 40)-net over F9, using
(125−67, 125, 182)-Net over F9 — Digital
Digital (58, 125, 182)-net over F9, using
- t-expansion [i] based on digital (50, 125, 182)-net over F9, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 50 and N(F) ≥ 182, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
(125−67, 125, 6317)-Net in Base 9 — Upper bound on s
There is no (58, 125, 6318)-net in base 9, because
- 1 times m-reduction [i] would yield (58, 124, 6318)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 21278 826662 048155 479924 523309 070994 182599 365991 972748 167502 370461 019793 806027 673307 331217 582269 858338 098356 709374 547825 > 9124 [i]