Best Known (33, 33+40, s)-Nets in Base 9
(33, 33+40, 81)-Net over F9 — Constructive and digital
Digital (33, 73, 81)-net over F9, using
- t-expansion [i] based on digital (32, 73, 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
(33, 33+40, 84)-Net in Base 9 — Constructive
(33, 73, 84)-net in base 9, using
- 2 times m-reduction [i] based on (33, 75, 84)-net in base 9, using
- base change [i] based on digital (8, 50, 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
- base change [i] based on digital (8, 50, 84)-net over F27, using
(33, 33+40, 128)-Net over F9 — Digital
Digital (33, 73, 128)-net over F9, using
- net from sequence [i] based on digital (33, 127)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 33 and N(F) ≥ 128, using
(33, 33+40, 3144)-Net in Base 9 — Upper bound on s
There is no (33, 73, 3145)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 4582 780345 307053 194038 356282 284987 739738 171815 075677 374599 212666 294049 > 973 [i]