MinT - Best Known (128−90, 128, s)-Nets in Base 9

Best Known (128−90, 128, s)-Nets in Base 9

(128−90, 128, 81)-Net over F₉ — Constructive and digital

Digital (38, 128, 81)-net over F₉, using

t-expansion [i] based on digital (32, 128, 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]

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

Digital (38, 128, 128)-net over F₉, using

t-expansion [i] based on digital (33, 128, 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]

(128−90, 128, 1113)-Net in Base 9 — Upper bound on s

There is no (38, 128, 1114)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 140 111175 446799 246222 760779 353859 042083 093613 676076 206519 532643 648209 135795 592887 271010 694305 770344 154862 507781 542752 143121 > 9¹²⁸ [i]