Best Known (64−33, 64, s)-Nets in Base 9
(64−33, 64, 84)-Net over F9 — Constructive and digital
Digital (31, 64, 84)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (2, 18, 20)-net over F9, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 2 and N(F) ≥ 20, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- digital (13, 46, 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 (2, 18, 20)-net over F9, using
(64−33, 64, 88)-Net in Base 9 — Constructive
(31, 64, 88)-net in base 9, using
- 2 times m-reduction [i] based on (31, 66, 88)-net in base 9, using
- base change [i] based on digital (9, 44, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- base change [i] based on digital (9, 44, 88)-net over F27, using
(64−33, 64, 123)-Net over F9 — Digital
Digital (31, 64, 123)-net over F9, using
(64−33, 64, 4852)-Net in Base 9 — Upper bound on s
There is no (31, 64, 4853)-net in base 9, because
- 1 times m-reduction [i] would yield (31, 63, 4853)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 1 313911 008575 689822 095802 675517 619833 944272 087994 391218 523265 > 963 [i]