Best Known (37, 37+40, s)-Nets in Base 9
(37, 37+40, 94)-Net over F9 — Constructive and digital
Digital (37, 77, 94)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (4, 24, 30)-net over F9, using
- net from sequence [i] based on digital (4, 29)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 4 and N(F) ≥ 30, using
- net from sequence [i] based on digital (4, 29)-sequence over F9, using
- digital (13, 53, 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 (4, 24, 30)-net over F9, using
(37, 37+40, 96)-Net in Base 9 — Constructive
(37, 77, 96)-net in base 9, using
- 1 times m-reduction [i] based on (37, 78, 96)-net in base 9, using
- base change [i] based on digital (11, 52, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- base change [i] based on digital (11, 52, 96)-net over F27, using
(37, 37+40, 138)-Net over F9 — Digital
Digital (37, 77, 138)-net over F9, using
(37, 37+40, 4886)-Net in Base 9 — Upper bound on s
There is no (37, 77, 4887)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 30 047492 837500 253882 979984 825697 893421 568103 984848 942658 248974 680313 242721 > 977 [i]