Best Known (64, 64+80, s)-Nets in Base 9
(64, 64+80, 165)-Net over F9 — Constructive and digital
Digital (64, 144, 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+80, 192)-Net over F9 — Digital
Digital (64, 144, 192)-net over F9, using
- t-expansion [i] based on digital (61, 144, 192)-net over F9, using
- net from sequence [i] based on digital (61, 191)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 61 and N(F) ≥ 192, using
- net from sequence [i] based on digital (61, 191)-sequence over F9, using
(64, 64+80, 5345)-Net in Base 9 — Upper bound on s
There is no (64, 144, 5346)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 258486 132021 955504 895578 117092 548023 035612 554666 237289 161306 587270 469056 551558 299617 734154 335292 108334 588128 128270 110881 997628 224478 909313 > 9144 [i]