MinT - Best Known (107−66, 107, s)-Nets in Base 9

Best Known (107−66, 107, s)-Nets in Base 9

(107−66, 107, 81)-Net over F₉ — Constructive and digital

Digital (41, 107, 81)-net over F₉, using

t-expansion [i] based on digital (32, 107, 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]

(107−66, 107, 140)-Net over F₉ — Digital

Digital (41, 107, 140)-net over F₉, using

t-expansion [i] based on digital (39, 107, 140)-net over F₉, using
- net from sequence [i] based on digital (39, 139)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 39 and N(F) ≥ 140, using
    - a curve from the manYPoints database [i]

(107−66, 107, 2023)-Net in Base 9 — Upper bound on s

There is no (41, 107, 2024)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 287126 236807 855712 347974 090533 236099 772319 620872 911345 672617 588267 047713 432282 004958 153949 226094 065473 > 9¹⁰⁷ [i]