MinT - Best Known (34, 34+78, s)-Nets in Base 9

Best Known (34, 34+78, s)-Nets in Base 9

(34, 34+78, 81)-Net over F₉ — Constructive and digital

Digital (34, 112, 81)-net over F₉, using

t-expansion [i] based on digital (32, 112, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(34, 34+78, 128)-Net over F₉ — Digital

Digital (34, 112, 128)-net over F₉, using

t-expansion [i] based on digital (33, 112, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(34, 34+78, 1034)-Net in Base 9 — Upper bound on s

There is no (34, 112, 1035)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 75397 780851 360255 183366 740929 078121 834403 630920 084219 297148 380240 308467 409805 411730 077826 136379 908617 786345 > 9¹¹² [i]