MinT - Best Known (118−86, 118, s)-Nets in Base 9

Best Known (118−86, 118, s)-Nets in Base 9

(118−86, 118, 81)-Net over F₉ — Constructive and digital

Digital (32, 118, 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]

(118−86, 118, 120)-Net over F₉ — Digital

Digital (32, 118, 120)-net over F₉, using

t-expansion [i] based on digital (31, 118, 120)-net over F₉, using
- net from sequence [i] based on digital (31, 119)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 31 and N(F) ≥ 120, using
    - a curve from the manYPoints database [i]

(118−86, 118, 850)-Net in Base 9 — Upper bound on s

There is no (32, 118, 851)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 40160 277847 769059 267693 487366 071996 954401 670757 243659 896784 890648 275612 589041 404146 606698 281484 503546 492446 523401 > 9¹¹⁸ [i]