Best Known (68−35, 68, s)-Nets in Base 9
(68−35, 68, 92)-Net over F9 — Constructive and digital
Digital (33, 68, 92)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 20, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- digital (13, 48, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- digital (3, 20, 28)-net over F9, using
(68−35, 68, 94)-Net in Base 9 — Constructive
(33, 68, 94)-net in base 9, using
- 1 times m-reduction [i] based on (33, 69, 94)-net in base 9, using
- base change [i] based on digital (10, 46, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- base change [i] based on digital (10, 46, 94)-net over F27, using
(68−35, 68, 130)-Net over F9 — Digital
Digital (33, 68, 130)-net over F9, using
(68−35, 68, 5162)-Net in Base 9 — Upper bound on s
There is no (33, 68, 5163)-net in base 9, because
- 1 times m-reduction [i] would yield (33, 67, 5163)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 8614 959029 141999 760711 449081 050488 033247 232739 576116 550932 331225 > 967 [i]