Best Known (97−57, 97, s)-Nets in Base 9
(97−57, 97, 81)-Net over F9 — Constructive and digital
Digital (40, 97, 81)-net over F9, using
- t-expansion [i] based on digital (32, 97, 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
(97−57, 97, 82)-Net in Base 9 — Constructive
(40, 97, 82)-net in base 9, using
- 2 times m-reduction [i] based on (40, 99, 82)-net in base 9, using
- base change [i] based on digital (7, 66, 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, 66, 82)-net over F27, using
(97−57, 97, 140)-Net over F9 — Digital
Digital (40, 97, 140)-net over F9, using
- t-expansion [i] based on digital (39, 97, 140)-net over F9, using
- net from sequence [i] based on digital (39, 139)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 39 and N(F) ≥ 140, using
- net from sequence [i] based on digital (39, 139)-sequence over F9, using
(97−57, 97, 2623)-Net in Base 9 — Upper bound on s
There is no (40, 97, 2624)-net in base 9, because
- 1 times m-reduction [i] would yield (40, 96, 2624)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 40 902030 534017 268523 507165 572576 008123 826011 240511 305228 919942 432423 442914 223928 862371 629057 > 996 [i]