Best Known (57, 57+65, s)-Nets in Base 9
(57, 57+65, 114)-Net over F9 — Constructive and digital
Digital (57, 122, 114)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (8, 40, 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, 82, 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, 40, 40)-net over F9, using
(57, 57+65, 182)-Net over F9 — Digital
Digital (57, 122, 182)-net over F9, using
- t-expansion [i] based on digital (50, 122, 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
(57, 57+65, 6467)-Net in Base 9 — Upper bound on s
There is no (57, 122, 6468)-net in base 9, because
- 1 times m-reduction [i] would yield (57, 121, 6468)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 29 184122 644339 664506 580215 950672 364675 493286 249115 266063 868868 615065 834105 849139 792869 190248 478360 170554 365570 784257 > 9121 [i]