MinT - Best Known (70, 140, s)-Nets in Base 9

Best Known (70, 140, s)-Nets in Base 9

(70, 140, 165)-Net over F₉ — Constructive and digital

Digital (70, 140, 165)-net over F₉, using

t-expansion [i] based on digital (64, 140, 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]

(70, 140, 261)-Net over F₉ — Digital

Digital (70, 140, 261)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 140, 11384)-Net in Base 9 — Upper bound on s

There is no (70, 140, 11385)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39 270711 233558 087653 954658 563670 223399 943820 621813 585561 419242 222287 772469 261454 014646 279282 063008 796170 850440 844845 316502 330268 664345 > 9¹⁴⁰ [i]