Best Known (31, 31+40, s)-Nets in Base 9
(31, 31+40, 78)-Net over F9 — Constructive and digital
Digital (31, 71, 78)-net over F9, using
- t-expansion [i] based on digital (22, 71, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
(31, 31+40, 82)-Net in Base 9 — Constructive
(31, 71, 82)-net in base 9, using
- 1 times m-reduction [i] based on (31, 72, 82)-net in base 9, using
- base change [i] based on digital (7, 48, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- base change [i] based on digital (7, 48, 82)-net over F27, using
(31, 31+40, 120)-Net over F9 — Digital
Digital (31, 71, 120)-net over F9, using
- net from sequence [i] based on digital (31, 119)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 31 and N(F) ≥ 120, using
(31, 31+40, 2521)-Net in Base 9 — Upper bound on s
There is no (31, 71, 2522)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 56 461031 592536 877915 030328 832413 948484 883789 925065 607479 853699 279041 > 971 [i]