MinT - Best Known (64, 143, s)-Nets in Base 9

Best Known (64, 143, s)-Nets in Base 9

(64, 143, 165)-Net over F₉ — Constructive and digital

Digital (64, 143, 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, 143, 192)-Net over F₉ — Digital

Digital (64, 143, 192)-net over F₉, using

t-expansion [i] based on digital (61, 143, 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, 143, 5714)-Net in Base 9 — Upper bound on s

There is no (64, 143, 5715)-net in base 9, because

1 times m-reduction [i] would yield (64, 142, 5715)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3199 500983 517467 702058 123825 849717 202501 794277 352972 568638 409335 944646 227878 946533 422969 928548 526139 071301 532267 137039 570486 002508 777129 > 9¹⁴² [i]