MinT - Best Known (133−86, 133, s)-Nets in Base 9

Best Known (133−86, 133, s)-Nets in Base 9

(133−86, 133, 81)-Net over F₉ — Constructive and digital

Digital (47, 133, 81)-net over F₉, using

t-expansion [i] based on digital (32, 133, 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]

(133−86, 133, 162)-Net over F₉ — Digital

Digital (47, 133, 162)-net over F₉, using

t-expansion [i] based on digital (46, 133, 162)-net over F₉, using
- net from sequence [i] based on digital (46, 161)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 46 and N(F) ≥ 162, using
    - a curve from the manYPoints database [i]

(133−86, 133, 1861)-Net in Base 9 — Upper bound on s

There is no (47, 133, 1862)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 364785 074187 381053 031684 142719 336491 441679 332965 402832 733246 988314 198043 433309 262824 617892 170265 824316 702373 186324 633695 105745 > 9¹³³ [i]