MinT - Best Known (38, 38+58, s)-Nets in Base 9

Best Known (38, 38+58, s)-Nets in Base 9

(38, 38+58, 81)-Net over F₉ — Constructive and digital

Digital (38, 96, 81)-net over F₉, using

t-expansion [i] based on digital (32, 96, 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]

(38, 38+58, 128)-Net over F₉ — Digital

Digital (38, 96, 128)-net over F₉, using

t-expansion [i] based on digital (33, 96, 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]

(38, 38+58, 2085)-Net in Base 9 — Upper bound on s

There is no (38, 96, 2086)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 40 634126 795378 088443 651889 615221 551365 038750 452902 027337 018630 467645 489956 996860 503522 405873 > 9⁹⁶ [i]