Best Known (66, 66+66, s)-Nets in Base 9
(66, 66+66, 165)-Net over F9 — Constructive and digital
Digital (66, 132, 165)-net over F9, using
- t-expansion [i] based on 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
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
(66, 66+66, 248)-Net over F9 — Digital
Digital (66, 132, 248)-net over F9, using
(66, 66+66, 10775)-Net in Base 9 — Upper bound on s
There is no (66, 132, 10776)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 914344 868311 665931 299262 924001 448996 552859 289664 226309 129689 353207 315475 464736 738565 955031 775102 803830 433345 317816 187685 443777 > 9132 [i]