MinT - Best Known (37, 97, s)-Nets in Base 9

Best Known (37, 97, s)-Nets in Base 9

(37, 97, 81)-Net over F₉ — Constructive and digital

Digital (37, 97, 81)-net over F₉, using

t-expansion [i] based on digital (32, 97, 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]

(37, 97, 128)-Net over F₉ — Digital

Digital (37, 97, 128)-net over F₉, using

t-expansion [i] based on digital (33, 97, 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]

(37, 97, 1814)-Net in Base 9 — Upper bound on s

There is no (37, 97, 1815)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 367 544107 619782 001213 105481 745346 974729 044997 199616 922974 886725 338773 269372 365342 593941 980305 > 9⁹⁷ [i]