Best Known (64, 64+68, s)-Nets in Base 9
(64, 64+68, 165)-Net over F9 — Constructive and digital
Digital (64, 132, 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
(64, 64+68, 219)-Net over F9 — Digital
Digital (64, 132, 219)-net over F9, using
(64, 64+68, 8551)-Net in Base 9 — Upper bound on s
There is no (64, 132, 8552)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 914018 239531 939666 074093 733362 483576 770286 755791 332791 675939 397702 761101 403277 238177 857037 606593 411436 847066 659304 928776 676225 > 9132 [i]