Best Known (69, 69+81, s)-Nets in Base 9
(69, 69+81, 165)-Net over F9 — Constructive and digital
Digital (69, 150, 165)-net over F9, using
- t-expansion [i] based on digital (64, 150, 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
(69, 69+81, 201)-Net over F9 — Digital
Digital (69, 150, 201)-net over F9, using
(69, 69+81, 7042)-Net in Base 9 — Upper bound on s
There is no (69, 150, 7043)-net in base 9, because
- 1 times m-reduction [i] would yield (69, 149, 7043)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 15223 897938 409151 110552 014010 680900 319249 368608 007285 435400 275646 760781 067660 941627 981747 568172 980021 166742 281067 711129 825864 425575 014657 275329 > 9149 [i]