Best Known (68, 68+73, s)-Nets in Base 9
(68, 68+73, 165)-Net over F9 — Constructive and digital
Digital (68, 141, 165)-net over F9, using
- t-expansion [i] based on digital (64, 141, 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
(68, 68+73, 226)-Net over F9 — Digital
Digital (68, 141, 226)-net over F9, using
(68, 68+73, 9152)-Net in Base 9 — Upper bound on s
There is no (68, 141, 9153)-net in base 9, because
- 1 times m-reduction [i] would yield (68, 140, 9153)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 39 309412 888414 472675 726840 221678 637986 342350 308308 931466 556603 014861 376637 247716 199531 700761 004226 043704 004655 013082 291255 190737 657505 > 9140 [i]