MinT - Best Known (112−74, 112, s)-Nets in Base 9

Best Known (112−74, 112, s)-Nets in Base 9

(112−74, 112, 81)-Net over F₉ — Constructive and digital

Digital (38, 112, 81)-net over F₉, using

t-expansion [i] based on digital (32, 112, 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]

(112−74, 112, 128)-Net over F₉ — Digital

Digital (38, 112, 128)-net over F₉, using

t-expansion [i] based on digital (33, 112, 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]

(112−74, 112, 1394)-Net in Base 9 — Upper bound on s

There is no (38, 112, 1395)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 76237 024138 613529 067334 223067 154706 050752 548366 816629 994536 028688 817492 556379 708407 794525 374364 998862 405625 > 9¹¹² [i]