MinT - Best Known (140−72, 140, s)-Nets in Base 9

Best Known (140−72, 140, s)-Nets in Base 9

(140−72, 140, 165)-Net over F₉ — Constructive and digital

Digital (68, 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]

(140−72, 140, 231)-Net over F₉ — Digital

Digital (68, 140, 231)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−72, 140, 9152)-Net in Base 9 — Upper bound on s

There is no (68, 140, 9153)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39 309412 888414 472675 726840 221678 637986 342350 308308 931466 556603 014861 376637 247716 199531 700761 004226 043704 004655 013082 291255 190737 657505 > 9¹⁴⁰ [i]