MinT - Best Known (125−90, 125, s)-Nets in Base 9

Best Known (125−90, 125, s)-Nets in Base 9

(125−90, 125, 81)-Net over F₉ — Constructive and digital

Digital (35, 125, 81)-net over F₉, using

t-expansion [i] based on digital (32, 125, 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]

(125−90, 125, 128)-Net over F₉ — Digital

Digital (35, 125, 128)-net over F₉, using

t-expansion [i] based on digital (33, 125, 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]

(125−90, 125, 958)-Net in Base 9 — Upper bound on s

There is no (35, 125, 959)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 196626 749365 037427 237578 868339 455283 509130 153648 964368 663366 900945 413154 872371 215464 277652 739529 859260 304841 430782 751897 > 9¹²⁵ [i]