Best Known (69, 69+71, s)-Nets in Base 9
(69, 69+71, 165)-Net over F9 — Constructive and digital
Digital (69, 140, 165)-net over F9, using
- t-expansion [i] based on digital (64, 140, 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+71, 245)-Net over F9 — Digital
Digital (69, 140, 245)-net over F9, using
(69, 69+71, 10690)-Net in Base 9 — Upper bound on s
There is no (69, 140, 10691)-net in base 9, because
- 1 times m-reduction [i] would yield (69, 139, 10691)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 4 364162 640015 817840 756523 911371 147135 792592 697086 282406 694987 227571 947647 219070 735063 521116 344642 217875 481222 094159 055848 245386 728905 > 9139 [i]