MinT - Best Known (65, 145, s)-Nets in Base 9

Best Known (65, 145, s)-Nets in Base 9

(65, 145, 165)-Net over F₉ — Constructive and digital

Digital (65, 145, 165)-net over F₉, using

t-expansion [i] based on digital (64, 145, 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, 145, 192)-Net over F₉ — Digital

Digital (65, 145, 192)-net over F₉, using

t-expansion [i] based on digital (61, 145, 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]

(65, 145, 5648)-Net in Base 9 — Upper bound on s

There is no (65, 145, 5649)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 322211 597448 763756 247639 532707 921637 063685 201360 797732 220311 962757 922872 126038 620279 900250 077118 056158 516976 345082 822913 072366 365976 571969 > 9¹⁴⁵ [i]