MinT - Best Known (116−84, 116, s)-Nets in Base 9

Best Known (116−84, 116, s)-Nets in Base 9

(116−84, 116, 81)-Net over F₉ — Constructive and digital

Digital (32, 116, 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]

(116−84, 116, 120)-Net over F₉ — Digital

Digital (32, 116, 120)-net over F₉, using

t-expansion [i] based on digital (31, 116, 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]

(116−84, 116, 866)-Net in Base 9 — Upper bound on s

There is no (32, 116, 867)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 510 918902 276925 476294 840019 017515 921639 521218 104267 893686 637423 287780 544630 974660 108297 492596 690404 842853 359985 > 9¹¹⁶ [i]