MinT - Best Known (70, 144, s)-Nets in Base 9

Best Known (70, 144, s)-Nets in Base 9

(70, 144, 165)-Net over F₉ — Constructive and digital

Digital (70, 144, 165)-net over F₉, using

t-expansion [i] based on digital (64, 144, 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, 144, 238)-Net over F₉ — Digital

Digital (70, 144, 238)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 144, 9453)-Net in Base 9 — Upper bound on s

There is no (70, 144, 9454)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 258078 869212 225742 945083 059646 940973 302421 383029 153173 203270 968307 827468 018546 282539 218608 540393 201233 988414 242094 382085 119410 313311 942065 > 9¹⁴⁴ [i]