MinT - Best Known (141−67, 141, s)-Nets in Base 9

Best Known (141−67, 141, s)-Nets in Base 9

(141−67, 141, 232)-Net over F₉ — Constructive and digital

Digital (74, 141, 232)-net over F₉, using

3 times m-reduction [i] based on digital (74, 144, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 72, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(141−67, 141, 328)-Net over F₉ — Digital

Digital (74, 141, 328)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−67, 141, 18369)-Net in Base 9 — Upper bound on s

There is no (74, 141, 18370)-net in base 9, because

1 times m-reduction [i] would yield (74, 140, 18370)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39 316359 553503 903062 117925 109128 858055 794852 953264 324183 167947 331150 855856 379819 094650 765863 728664 537950 376037 801110 211023 197904 505873 > 9¹⁴⁰ [i]