Best Known (47, 116, s)-Nets in Base 9
(47, 116, 81)-Net over F9 — Constructive and digital
Digital (47, 116, 81)-net over F9, using
- t-expansion [i] based on digital (32, 116, 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
(47, 116, 84)-Net in Base 9 — Constructive
(47, 116, 84)-net in base 9, using
- 1 times m-reduction [i] based on (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
- base change [i] based on digital (8, 78, 84)-net over F27, using
(47, 116, 162)-Net over F9 — Digital
Digital (47, 116, 162)-net over F9, using
- t-expansion [i] based on digital (46, 116, 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
(47, 116, 2836)-Net in Base 9 — Upper bound on s
There is no (47, 116, 2837)-net in base 9, because
- 1 times m-reduction [i] would yield (47, 115, 2837)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 54 889578 167013 255330 444022 749330 390737 842600 805271 067042 165433 404743 831253 730869 987649 047064 358005 587547 173905 > 9115 [i]