MinT - Best Known (34, 34+58, s)-Nets in Base 9

Best Known (34, 34+58, s)-Nets in Base 9

(34, 34+58, 81)-Net over F₉ — Constructive and digital

Digital (34, 92, 81)-net over F₉, using

t-expansion [i] based on digital (32, 92, 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+58, 128)-Net over F₉ — Digital

Digital (34, 92, 128)-net over F₉, using

t-expansion [i] based on digital (33, 92, 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+58, 1535)-Net in Base 9 — Upper bound on s

There is no (34, 92, 1536)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6189 167147 912195 663011 454902 660453 020817 805772 316040 059357 246624 104568 970419 751817 179137 > 9⁹² [i]