MinT - Best Known (64, 144, s)-Nets in Base 9

Best Known (64, 144, s)-Nets in Base 9

(64, 144, 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
- Niederreiterâ€“Xing sequence constructionÂ 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]

(64, 144, 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
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 61 and N(F) ≥ 192, using
    - Drinfeld modules of rank 1 [i]

(64, 144, 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 9^mÂ â‰¥ 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]