MinT - Best Known (54, 54+49, s)-Nets in Base 9

Best Known (54, 54+49, s)-Nets in Base 9

(54, 54+49, 232)-Net over F₉ — Constructive and digital

Digital (54, 103, 232)-net over F₉, using

1 times m-reduction [i] based on digital (54, 104, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 52, 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]

(54, 54+49, 250)-Net over F₉ — Digital

Digital (54, 103, 250)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+49, 13910)-Net in Base 9 — Upper bound on s

There is no (54, 103, 13911)-net in base 9, because

1 times m-reduction [i] would yield (54, 102, 13911)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21 523346 039013 265381 305622 591374 733769 362466 197783 432342 213630 052635 859892 963845 173277 160647 624001 > 9¹⁰² [i]