Best Known (30, 30+32, s)-Nets in Base 9
(30, 30+32, 80)-Net over F9 — Constructive and digital
Digital (30, 62, 80)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (1, 17, 16)-net over F9, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 1 and N(F) ≥ 16, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- digital (13, 45, 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 (1, 17, 16)-net over F9, using
(30, 30+32, 88)-Net in Base 9 — Constructive
(30, 62, 88)-net in base 9, using
- 1 times m-reduction [i] based on (30, 63, 88)-net in base 9, using
- base change [i] based on digital (9, 42, 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, 42, 88)-net over F27, using
(30, 30+32, 120)-Net over F9 — Digital
Digital (30, 62, 120)-net over F9, using
(30, 30+32, 4228)-Net in Base 9 — Upper bound on s
There is no (30, 62, 4229)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 145950 158205 867513 796049 559720 108626 751525 786243 954163 852417 > 962 [i]