MinT - Best Known (116−37, 116, s)-Nets in Base 9

Best Known (116−37, 116, s)-Nets in Base 9

(116−37, 116, 740)-Net over F₉ — Constructive and digital

Digital (79, 116, 740)-net over F₉, using

10 times m-reduction [i] based on digital (79, 126, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 63, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(116−37, 116, 2138)-Net over F₉ — Digital

Digital (79, 116, 2138)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−37, 116, 1179194)-Net in Base 9 — Upper bound on s

There is no (79, 116, 1179195)-net in base 9, because

1 times m-reduction [i] would yield (79, 115, 1179195)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 54 687910 865596 823469 165082 061131 064736 516954 226906 077138 381791 733813 614832 668408 316604 576225 368923 573075 326897 > 9¹¹⁵ [i]