Best Known (75, 75+74, s)-Nets in Base 9
(75, 75+74, 165)-Net over F9 — Constructive and digital
Digital (75, 149, 165)-net over F9, using
- t-expansion [i] based on digital (64, 149, 165)-net over F9, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
(75, 75+74, 283)-Net over F9 — Digital
Digital (75, 149, 283)-net over F9, using
(75, 75+74, 12729)-Net in Base 9 — Upper bound on s
There is no (75, 149, 12730)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 15232 197715 270915 149988 102386 983034 724570 957836 857510 878821 092547 437787 882786 083107 863724 416404 021467 634731 474516 713014 827507 715823 976411 222161 > 9149 [i]