Best Known (117−70, 117, s)-Nets in Base 9
(117−70, 117, 81)-Net over F9 — Constructive and digital
Digital (47, 117, 81)-net over F9, using
- t-expansion [i] based on digital (32, 117, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
(117−70, 117, 84)-Net in Base 9 — Constructive
(47, 117, 84)-net in base 9, using
- base change [i] based on digital (8, 78, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
(117−70, 117, 162)-Net over F9 — Digital
Digital (47, 117, 162)-net over F9, using
- t-expansion [i] based on digital (46, 117, 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
(117−70, 117, 2670)-Net in Base 9 — Upper bound on s
There is no (47, 117, 2671)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 4450 200795 949549 714910 242719 627889 309091 433933 786758 215800 716261 809481 319184 673613 668100 766168 893906 665129 095017 > 9117 [i]