MinT - Best Known (65, 65+67, s)-Nets in Base 9

Best Known (65, 65+67, s)-Nets in Base 9

(65, 65+67, 165)-Net over F₉ — Constructive and digital

Digital (65, 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
  - 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]

(65, 65+67, 233)-Net over F₉ — Digital

Digital (65, 132, 233)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+67, 10079)-Net in Base 9 — Upper bound on s

There is no (65, 132, 10080)-net in base 9, because

1 times m-reduction [i] would yield (65, 131, 10080)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 101402 766405 306815 371650 914447 050013 128954 323067 312620 692842 587177 995568 066981 953921 806513 572901 315786 678362 741864 572482 706177 > 9¹³¹ [i]