Best Known (68, 68+68, s)-Nets in Base 9
(68, 68+68, 165)-Net over F9 — Constructive and digital
Digital (68, 136, 165)-net over F9, using
- t-expansion [i] based on digital (64, 136, 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+68, 255)-Net over F9 — Digital
Digital (68, 136, 255)-net over F9, using
(68, 68+68, 11080)-Net in Base 9 — Upper bound on s
There is no (68, 136, 11081)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 6000 519037 129137 607516 187602 588761 760042 349853 297340 894828 104116 821097 344685 045128 005599 244072 253124 673344 254225 738412 006407 478481 > 9136 [i]