MinT - Best Known (30, 30+62, s)-Nets in Base 9

Best Known (30, 30+62, s)-Nets in Base 9

(30, 30+62, 78)-Net over F₉ — Constructive and digital

Digital (30, 92, 78)-net over F₉, using

t-expansion [i] based on digital (22, 92, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(30, 30+62, 110)-Net over F₉ — Digital

Digital (30, 92, 110)-net over F₉, using

t-expansion [i] based on digital (26, 92, 110)-net over F₉, using
- net from sequence [i] based on digital (26, 109)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 26 and N(F) ≥ 110, using
    - a curve from the manYPoints database [i]

(30, 30+62, 1035)-Net in Base 9 — Upper bound on s

There is no (30, 92, 1036)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6291 185116 565188 554479 004847 852486 250379 648133 086762 889636 214619 026322 303343 398641 225505 > 9⁹² [i]